A tall space with a small bottom

István Juhász*, Saharon Shelah, Lajos Soukup, Zoltán Szentmiklóssy

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

We introduce a general method of constructing locally compact scattered spaces from certain families of sets and then, with the help of this method, we prove that if κ = κ, then there is such a space of height κ+ with only κ many isolated points. This implies that there is a locally compact scattered space of height ω2 with ω1 isolated points in ZFC, solving an old problem of the first author.

Original languageEnglish
Pages (from-to)1907-1916
Number of pages10
JournalProceedings of the American Mathematical Society
Volume131
Issue number6
DOIs
StatePublished - Jun 2003

Keywords

  • Locally compact scattered space
  • Superatomic Boolean algebra

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