Gently Killing S--spaces

1998/12/22 by Todd Eisworth, Eisworth, Todd, Peter Nyikos +3
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO) #Rings, Modules, and Algebras #math.GN #math.LO

paper · pdf · doi:10.48550/arxiv.math/9812133

published as Israel J. Math. 136 (2003) 189--220

arxiv created 1998/12/22 · openalex publication_date 1998/12/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We produce a model of ZFC in which there are no locally compact first countable S-spaces, and in which 2^aleph₀<2^aleph₁. A consequence of this is that in this model there are no locally compact, separable, hereditarily normal spaces of size aleph₁, answering a question of the second author.

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