# Sh:454

• Shelah, S. (1993). Number of open sets for a topology with a countable basis. Israel J. Math., 83(3), 369–374.
• 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.
• published version (6p)
Bib entry
@article{Sh:454,
author = {Shelah, Saharon},
title = {{Number of open sets for a topology with a countable basis}},
journal = {Israel J. Math.},
fjournal = {Israel Journal of Mathematics},
volume = {83},
number = {3},
year = {1993},
pages = {369--374},
issn = {0021-2172},
mrnumber = {1239070},
mrclass = {54A25 (54A05 54H05)},
doi = {10.1007/BF02784064},
note = {\href{https://arxiv.org/abs/math/9308217}{arXiv: math/9308217}},
arxiv_number = {math/9308217}
}