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The Works of Bronisław Knaster (1893–1980) in Continuum Theory

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Handbook of the History of General Topology

Part of the book series: History of Topology ((HIPO,volume 1))

Abstract

The principal area of the mathematical research of Bronisław Knaster (see the bibliography enclosed with this article) was geometric topology, and his main object of interest was connectedness. The greater part of this topic was related to the study of continua, which were then defined as closed and connected subsets of a Euclidean space, and were not necessarily compact.

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Bibliography of the works of Bronisław Knaster

  1. Bronisław Knaster: Bronisław Knaster: (with K. Kuratowski) Sur les ensembles connexes, Fundamenta Mathematicae 2 (1921), 206–255.

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  2. Bronisław Knaster: Bronisław Knaster: (with W. Sierpiriski) Sur une ensemble abstrait, dont chaque élément est un élément limite de chaque sous ensemble non dénombrable, Fundamenta Mathematicae 3 (1922), 35–40.

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  3. Bronisław Knaster: Bronisław Knaster: Un continu dont tout sous-continu est indécomposable, Fundamenta Mathematicae 3 (1922), 247–286.

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  4. Bronisław Knaster: Bronisław Knaster: (with K. Kuratowski) Sur les continus non bornés, Fundamenta Mathematicae 5 (1924), 23–58.

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  5. Bronisław Knaster: Bronisław Knaster: Sur un problème de M. R. L. Wilder, Fundamenta Mathematicae 7 (1925), 191–197.

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  6. Quelques coupures singulières du plan, Fundamenta Mathematicae 7 (1925), 264–289.

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  7. Sur quelques propriétés topologiques des functions dérivées, Rendiconti del Circolo Matematico di Palermo 49 (1925), 382–386.

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  8. Bronisław Knaster: Sur les ensembles connexes irréductibles entre deux points, Fundamenta Mathematicae 10 (1927), 276–297.

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  9. Remark on a theorem of R. L. Moore, Proceedings of the National Academy of Sciences U.S.A. 13 (1927), 647–649.

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  10. Bronisław Knaster: (with K. Kuratowski)A connected and connected im kleinen point set which contains no perfect subset, Bulletin of the American Mathematical Society 33 (1927), 106–109.

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  11. Bronisław Knaster: Decomposizioni continue e semicontinue nell’Analysis Situs, Atti del Congresso Internazionale dei Matematici in Bologna,1928, tomo II, 221–224.

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  12. Bronisław Knaster: Sui punti regolari nelle curve di Jordan, Atti del Congresso Internazionale dei Matematici in Bologna,1928, tomo II, 225–227.

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  13. Bronisław Knaster: Sur les continus que tout sous-continu divise, Ksigga Pamigtkowa I Polskiego Zjazdu Matematycznego we Lwowie [Memorial Book of the First Polish Mathematical Congress], Lwów 1929, 59–64.

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  14. Bronisław Knaster: Einige Probleme über Punktmengen mit Fixpunkten, Comptes-Rendus du Premier Congrès des Mathématiciens des Pays Slaves, Warszawa 1929, 287–290.

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  15. Ein Beweis des Fixpunktsatzes für ri-dimensionale Simplexe, Fundamenta Mathematicae 14 (1929), 132–137.

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  16. Über eindimensional unvergleichbare Kontinua, Anzeiger Wiener Akademie der Wissenschaften, Math.-naturwiss. Kl. Nr 10 (1930), 1–2.

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  17. Bronisław Knaster: Ein Zerlegungssatz über unikohärente continua, Verhandlungen des Internationalen Mathematikerkongress in Zürich, Zürich 1932, 193–194.

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  18. Bronisław Knaster: Pfehled teorie nerozlozitelnÿch kontinui [Survey of the theory of indecomposable continua], Casopis pro péstovâni matematiky a fizyky 62 (1933), 310–337. [in Czech; French summary].

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  19. Bronisław Knaster: (with S. Mazurkiewicz) Sur un problème concernant les transformations continues, Fundamenta Mathematicae 21 (1933), 85–90.

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  20. Bronisław Knaster: (with W. Hurewicz) Ein Einbettungssatz über henkelfreie Kontinua, Proceedings of the Section of Sciences, Koninklijke Akademie van Wetenschappen te Amsterdam 36 (1933), 557–560.

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  21. Bronisław Knaster: Un continu irréductible à décomposition continue en tranches, Fundamenta Mathematicae 25 (1935), 58–577.

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  22. Bronisław Knaster: Über rationale Kurven ohne Bögen, Monatshefte für Mathematik und Physik 42 (1935), 37–44.

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  23. Bronisław Knaster: Sur une propriété caractéristique de l’ensemble des nombres réels, Matematicheskii SbornikAkademii Nauk SSSR 16 (58) (1945), 281–290.

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  24. Bronisław Knaster: Sur un problème de R. Alexandroff, Fundamenta Mathematicae 33 (1945), 308–313.

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  25. Bronisław Knaster: Sur les coupures biconnexes des espaces euclidiens de dimension n = 1 arbitraire, Matematicheskii Sbornik Akademii Nauk SSSR 19 (61) (1946), 9–18. [in Russian; loose French summary].

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  26. Bronisław Knaster: with H. Steinhaus) Sur les partage pragmatique, Comptes Rendus de la Société des Sciences et des Lettres de Wroclaw 2 (1947), 1–13.

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  27. Bronisław Knaster: O drukarniach naukowych w Polsce [On scientific printing houses in Poland], Casopis pro péstovCni matematiky a fizyky 74 (1949), 341–346. [in Polish]

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  28. Bronisław Knaster: O aplikacich matematické logiky na matematiku [On applications of mathematical logic in mathematics], Casopis pro péstovkni matematiky a fizyky 76 (1951) 3–22. [in Czech].

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  29. Bronisław Knaster: Sur une équivalence pour les fonctions, Colloquium Mathematicum 2 (1951), 1–4.

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  30. Bronisław Knaster: Un théorème sur la compactification, Annales de la Société Polonaise de Mathématique 25 (1952), 252–267.

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  31. Bronisław Knaster: (with M. Reichbach)Sur la caractérisation topologique de l’ensemble des bouts d’une courbe, Fundamenta Mathematicae 40 (1953), 13–28.

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  32. Bronisław Knaster: (with M. Reichbach) Un lemme sur les F-sigma, Fundamenta Mathematicae 40 (1953), 172–179.

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  33. Bronisław Knaster: (with M. Reichbach) Notion d’homogénéité et prolongements des homéomorphies, Fundamenta Mathematicae 40 (1953), 180–193.

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  34. Bronisław Knaster: (with K. Urbanik) Sur les espaces complets séparables de dimension 0, Fundamenta Mathematicae 40 (1953), 194–202.

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  35. Bronisław Knaster: Wspomnienie o Samuelu Dicksteinie [Samuel Dickstein — a memoir], Prace Matematyczne 1 (1955), 4–8. [in Polish]

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  36. with J. Mioduszewski and K. Urbanik) Points-limites et points de continuité, Colloquium Mathematicum 3 (1955), 164–169.

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  37. K37] Bronisław Knaster: Sur la fixation des décompositions, Bulletin de l’Académie Polonaise des Sciences, Cl. III,4 (1956) 193–196 . [a version in Russian on pp. 189–192] Bronisław Knaster: .

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  38. Bronisław Knaster: (with A. Lelek) Coutures et tapis, Fundamenta Mathematicae 45 (1958), 186–199.

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  39. Bronisław Knaster: (with J. Mioduszewski Division des régions partielles par les frontières et des frontières par les points, Fundamenta Mathematicae 45 (1958), 306–313.

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  40. Bronisław Knaster: (with A. Lelek and J. Mycielski) Sur les décompositions d’ensembles connexes, Colloquium Mathematicum 6 (1958), 227–246.

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  41. Bronisław Knaster: Eduard tech (1893–1960), Sprawozdania Wroctawskiego Towarzystwa Naukowego 15 B (1960), 6 –13. [in Polish].

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  42. Bronisław Knaster: 101 posiedzenie naukowe Wydzialu Nauk Matematycznych i Przyrodniczych [101St scientific meeting of the Section of Mathematical and Natural Sciences], Sprawozdania Wroctawskiego Towarzystwa Naukowego 15 B (1960), 14–16. [in Polish].

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  43. Bronisław Knaster: Zygmunt Janiszewski (1888–1920) [Preface in the book: Z. Janiszewski, Oeuvres choisies],PWN, Warszawa 1961; pp. 5–16. [in French; Polish translation in: Wiadomosci Matematyczne 4 (1960), 1–9.

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  44. Bronisław Knaster: O pracach topologicznych katedry geometrii Uniwersytetu Wroclawskiego i seminarium topologii Instytutu Matematycznego PAN, Czggé I [On topological papers of the Chair of Geometry of the University of Wroclaw and Topological Seminar of the Mathematical Institute of the Polish Academy of Sciences, Part I], Sprawozdania Wroclawskiego Towarzystwa Naukowego 16B (1961), 6–7; Czggé II [Part II] ibidem,22. [in Polish].

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  45. Bronisław Knaster: Karol Borsuk, Nauka Polska 3 1964, 61–65. [in Polish].

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  46. Bronisław Knaster: (with S. Bergman, R. Duda, J. Mycielski and A. Schinzel) Kazimierz Zarankiewicz, Colloquium Mathematicum 12 (1964), 277–288. [in French; Polish translation in: Wiadomosci Matematyczne 9 (1967), 175–185.

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  47. Bronisław Knaster: Une décomposition effective du carré en deux ensembles denses, ponctiformes, connexes et localement connexes, Commentationes Mathematicae (Prace Matematyczne) 14 (1970), 19–23.

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  48. Bronisław Knaster: Poglady Stanislawa Kulczyrískiego na rolg matematyki w naukach przyrodniczych [Stanislaw Kulczyríski’s opinions on role of mathematics in natural sciences], Sprawozdania Wroclawskiego Towarzystwa Naukowego 30 A (1975), Dodatek 1, 126–127. [in Polish].

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  49. Bronisław Knaster: A singular plane curve, Colloquium Mathematicum 42 (1979), 263–271.

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  50. Bronisław Knaster: Sur un problème de M. L. Vietoris, Annales de la Société Polonaise de Mathématique 5 (1926), 102. [a report].

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  51. Sur la théorie des dimensions de Menger-Urysohn, Annales de la Société Polonaise de Mathématique 6 (1927), 121–122. [a report].

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  52. Bronisław Knaster: Un théorème sur trois continus plans, Annales de la Société Polonaise de Mathématique 6 (1927), 131. [a report].

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  53. Bronisław Knaster: Un théorème sur les fonctions d’ensemble, Annales de la Société Polonaise de Mathématique 6 (1927), 133–134. [a report].

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  54. Bronisław Knaster: Sur une courbe ne contenant aucune image continue d’intervalle ni aucun continu indécomposable, Comptes-Rendus du Premier Congrès des Mathématiciens des Pays Slaves,Warszawa 1929, 290. [an announcement].

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  55. Une fonction réelle continue de deux variables qui n’est constante sur aucun arc simple [Announcement at the All-Union Congress on the Theory of Functions held in Kiev, 24–26 June 1940] Bronisław Knaster: .

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  56. Sur une propriété caractéristique de l’ensemble des nombres réelles, List of the works achieved in the field of mathematics and sciences in Poland during the German occupation, 1939–1945, Polish Academy of Sciences and Letters,Krakow 1947, 224–225. [a report on [K23] Bronisław Knaster: ].

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  57. Bronisław Knaster: Une fonction réelle continue de deux variables réelles qui n’est constante sur aucun arc simple, List of the works achieved in the field of mathematics and sciences in Poland during the German occupation, 1939–1945, Polish Academy of Sciences and Letters,Krakow 1947, 225. [a report on [K55] Bronisław Knaster: ].

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  58. Bronisław Knaster: Sur les coupures biconnexes des espaces euclidiens de dimension ri 1 arbitraire, List of the works achieved in the field of mathematics and sciences in Poland during the German occupation, 1939–1945, Polish Academy of Sciences and Letters,Krakow 1947, 225–227.

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  59. Bronisław Knaster: Sur les ensembles connexes, Annales de la Société Polonaise de Mathématique 19 (1946), 223. [a report].

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  60. Bronisław Knaster: Sur le problème du partage pragmatique de H. Steinhaus, Annales de la Société Polonaise de Mathématique 19 (1946 ), 228–230. [a report; loose summary of [K26] [also: Colloquium Mathematicum 1 (1948), 36].

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  61. Bronisław Knaster: Sur les transformations continues des sphères en hyperplans de dimension inférieure, Annales de la Société Polonaise de Mathématique 19 (1946), 232. [a report] [also: Colloquium Mathematicum 1 (1948), 37.

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  62. Bronisław Knaster: (with H. Steinhaus) O podziale pragmatycznym, Sprawozdania Wroctawskiego Towarzystwa Naukowego 2 (1947), 81–82. [in Polish; a summary of [K26].

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  63. Bronisław Knaster: Rapport du voyage de Tchecoslovaquie, Colloquium Mathematicum 1 (1948), 41–42. [a report].

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  64. Bronisław Knaster: Un problème sur les bandes inscrites, Gasopis pro péstovkni matematiky a fizyky 74 (1949), 236–237. [an announcement].

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  65. Bronisław Knaster: N. I. Lobatchewsky, Colloquium Mathematicum 2 (1951), 159. [a report].

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  66. Sur l’ensemble des points d’orde 1 au sens de Menger, Colloquium Mathematicum 2 (1951), 311. [a report].

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  67. Bronisław Knaster: Sur un problème de Borsuk, Colloquium Mathematicum 2 (1951), 323. [a report].

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  68. Bronisław Knaster: Sur un continu irréductible construit par J. Mioduszewski, Colloquium Mathematicum 3 (1955), 82. [a report].

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  69. Bronisław Knaster: Un théorème sur la compactification, Colloquium Mathematicum 3 (1955), 188. [a report].

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  70. Bronisław Knaster: (with M. Reichbach) Un lemme sur les F-sigma, Colloquium Mathematicum 3 (1955), 200. [a report]also: Prace Matematyczne 1 (1955), 194.

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  71. Bronisław Knaster: Un problème sur la piste des faces d’un tertaèdre roulant sur le plan, Colloquium Mathematicum 3 (1955), 203. [a report].

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  72. Bronisław Knaster: (with K. Urbanik) Sur les espaces complets de dimension 0, Colloquium Mathematicum 3 (1955), 206. [a report] also: Prace Matematyczne 1 (1955), 198.

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  73. Bronisław Knaster: (with J. Mioduszewski and K. Urbanik) Points-limites et points de continuité, Colloquium Mathematicum 3 (1955), 210. [a report] [also: Prace Matematyczne 1 (1955), 200 .

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  74. Bronisław Knaster: Un théorème sur les décompositions semi-continues, Colloquium Mathematicum 4 (1957), 137. [a report].

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  75. Bronisław Knaster: Sur certaines bases dans les cubes a n dimensions, Colloquium Mathematicum 4 (1957), 138–139. [a report].

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  76. Sur le problème du rapport entre fixation et enfilage, Colloquium Mathematicum 4 (1957), 267. [a report] also: Prace Matematyczne 2 (1958), 197.

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  77. Bronisław Knaster: (with J. Mioduszewski) O dzieleniu obszarów czgsciowych przez brzegi i brzegow przez punkty [On divisions of partial regions by boundaries and boundaries by points], Prace Matematyczne 4 (1960), 137. [a report].

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  78. Bronisław Knaster: (with K. Kuratowski) Problème 2, Fundamenta Mathematicae 1 (1920), 223.

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  79. Bronisław Knaster: (with K. Kuratowski) Problème 15, Fundamenta Mathematicae 2 (1921), 286.

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  80. Bronisław Knaster: (with K. Zarankiewicz) Problème 42, Fundamenta Mathematicae 8 ( 1926, 376.

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  81. Bronisław Knaster: Problème 43, Fundamenta Mathematicae 8 (1926), 376.

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  82. Bronisław Knaster: Problème P 4, Colloquium Mathematicum 1 (1948), 30–31.

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  83. Bronisław Knaster: Problème P 65, Colloquium Mathematicum 2 (1951), 60. [K841 Problème P 100, Colloquium Mathematicum 2 (1951), 301.

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  84. Bronisław Knaster: Problème P 123, Colloquium Mathematicum 3 (1955), 74.

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  85. Bronisław Knaster: with J. Mioduszewski and K. Urbanik) Problème P 132, Colloquium Mathematicum 3 (1955), 170.

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  86. Bronisław Knaster: Problèmes P 148 et 149, Colloquium Mathematicum 4 (1957), 89–90.

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  87. Bronisław Knaster: Problèmes P 177 et 178, Colloquium Mathematicum 4 (1957), 243.

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  88. Bronisław Knaster: Problème P 195, Colloquium Mathematicum 5 (1958), 117.

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  89. Bronisław Knaster: Problèmes P 201 - P 204, Colloquium Mathematicum 5 (1958), 118.

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  90. Bronisław Knaster: Problèmes P 222 - P 224, Colloquium Mathematicum 5 (1958), 234–235.

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  91. Bronisław Knaster: Problème P 253, Colloquium Mathematicum 6 (1958), 332.

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  92. Bronisław Knaster: Problèmes P 264 - P 266, Colloquium Mathematicum 6 (1958), 334–335.

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  93. Bronisław Knaster: (with A. Lelek) Problème P 267, Colloquium Mathematicum 6 (1958), 335.

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  94. Bronisław Knaster: (with A. Lelek)Problème P 281, Colloquium Mathematicum 7 (1960), 108.

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  95. Problème P 284, Colloquium Mathematicum 7 (1960), 108.

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  96. Bronisław Knaster: (with A. Lelek) Problème P 290, Colloquium Mathematicum 7 (1960), 110.

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  97. Bronisław Knaster: Problème P 304, Colloquium Mathematicum 7 (1960), 310.

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  98. Bronisław Knaster: Problèmes P 323 et P 324, Colloquium Mathematicum 8 (1961), 139.

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  99. Bronisław Knaster: Problème P 340, Colloquium Mathematicum 8 (1961), 278.

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  100. Bronisław Knaster: Exercise 322, Matematyka 3(25) (1953), 54 and 6 (34) (1954), 109. [in Polish]

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  101. Bronisław Knaster: Problème P 370, Colloquium Mathematicum 9 (1962), 169.

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  102. Bronisław Knaster: Problèmes P 480 et P 481, Colloquium Mathematicum 12 (1964), 294–295.

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  103. Bronisław Knaster: Problème P 554, Colloquium Mathematicum 15 (1966), 160.

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  104. Bronisław Knaster: Problème P 562, Colloquium Mathematicum 15 (1966), 320.

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  105. Bronisław Knaster: Problème P 683, Colloquium Mathematicum 21 (1970), 163.

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  106. Bronisław Knaster: Problème P 737, Colloquium Mathematicum 23 (1971), 178–179.

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  107. Bronisław Knaster: Problème P 846, Colloquium Mathematicum 27 (1973), 332.

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  108. Bronisław Knaster: Problème P 1138, Colloquium Mathematicum 42 (1979), 396.

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  109. Bronisław Knaster: Problem 69 in: Continua, with the Houston problem book, H. Cook, W. T. Ingram, K. T. Kuperberg, A. Lelek and P. Minc (editors), M. Dekker 1995; p. 378.

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  110. Bronisław Knaster: Problem 126 in: Continua, with the Houston problem book, H. Cook, W. T. Ingram, K. T. Kuperberg, A. Lelek and P. Mine (editors), M. Dekker 1995; p. 385.

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Authors and Affiliations

  1. Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384, Wrocław, Poland

    Janusz J. Charatonik

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  1. Janusz J. Charatonik
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  1. Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, USA

    C. E. Aull

  2. Department of Mathematics and Computer Science, University of Antwerp, RUCA, Antwerp, Belgium

    R. Lowen

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Charatonik, J.J. (1997). The Works of Bronisław Knaster (1893–1980) in Continuum Theory. In: Aull, C.E., Lowen, R. (eds) Handbook of the History of General Topology. History of Topology, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0468-7_5

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  • DOI: https://doi.org/10.1007/978-94-017-0468-7_5

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