Cardinalities of topologies with small base

Saharon Shelah*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 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 base of cardinality ≤μ, λ≤μ<2λ, λ strong limit of cofinality א0, then T has cardinality ≤μ or ≥2λ. This is our main conclusion (21). In Theorem 2 we prove it under some set-theoretic assumption, which is clear when λ = μ; then we eliminate the assumption by a theorem on pcf from [Sh 460] motivated originally by this. Next we prove that the simplest examples are the basic ones; they occur in every example (for λ = א0 this fulfills a promise from [Sh 454]). The main result for the case λ = א0 was proved in [Sh 454].

Original languageEnglish
Pages (from-to)95-113
Number of pages19
JournalAnnals of Pure and Applied Logic
Volume68
Issue number1
DOIs
StatePublished - 9 Jun 1994

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