Number of open sets for a topology with a countable basis

Saharon Shelah

doi:10.1007/BF02784064

Number of open sets for a topology with a countable basis

Saharon Shelah^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Let T be the family of open subsets of a topological space (not necessarily Hausdorff or even T₀). We prove that if T has a countable base and is not countable, then T has cardinality at least continuum.

Original language	English
Pages (from-to)	369-374
Number of pages	6
Journal	Israel Journal of Mathematics
Volume	83
Issue number	3
DOIs	https://doi.org/10.1007/BF02784064
State	Published - Oct 1993

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title = "Number of open sets for a topology with a countable basis",

abstract = "Let T be the family of open subsets of a topological space (not necessarily Hausdorff or even T 0). We prove that if T has a countable base and is not countable, then T has cardinality at least continuum.",

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Number of open sets for a topology with a countable basis

Abstract

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