Weaker connected and weaker nowhere locally compact topologies for metrizable and similar spaces

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Abstract

We prove that any metrizable non-compact space has a weaker metrizable nowhere locally compact topology. As a consequence, any metrizable non-compact space has a weaker Hausdorff connected topology. The same is established for any Hausdorff space X with a σ-locally finite base whose weight w(X) is a successor cardinal.

MSC

54A10
54D05
54E35
54C05
54E40
54E45

Keywords

Metrizable space
Nowhere locally compact space
Connected space
Condensation

Cited by (0)

1

Research supported by Consejo Nacional de Ciencia y Tecnologı́a (CONACYT) de México, grant 400200-5-3012P-E.

2

Research of the first author also partially supported by National Science Foundation grant DMS 970-4849.