English

Number of open sets for a topology with a countable basis

Logic 2008-02-03 v1 General Topology

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.

Keywords

Cite

@article{arxiv.math/9308217,
  title  = {Number of open sets for a topology with a countable basis},
  author = {Saharon Shelah},
  journal= {arXiv preprint arXiv:math/9308217},
  year   = {2008}
}
R2 v1 2026-07-22T17:54:26.532Z