Sh:454

• Shelah, S. (1993). Number of open sets for a topology with a countable basis. Israel J. Math., 83(3), 369–374. arXiv: math/9308217 DOI: 10.1007/BF02784064 MR: 1239070
• 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.
• Version 1993-08-29_10 (6p) published version (6p)

@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}
}