Pseudocompact Δ -spaces are often scattered

A. Leiderman, V. V. Tkachuk

Research output: Contribution to journalArticlepeer-review

Abstract

Given a pseudocompact Δ-space X, we establish that countable subsets of X must be scattered. This implies that pseudocompact Δ-spaces of countable tightness are scattered. If a pseudocompact Δ-space has the Souslin property, then it is separable and has a dense set of isolated points. It is shown that adding a countable subspace to a pseudocompact Δ-space can destroy the Δ-property. However, if X is countably compact and Y⊂ X is a Δ-space for some Y⊂ X such that | X\ Y| ≤ ω, then X is a Δ-space. We also show that monotonically normal Δ-spaces must be hereditarily paracompact. Besides, if X is a subspace of an ordinal with its order topology, then X is hereditarily paracompact if and only if it has the Δ-property.

Original languageEnglish
Pages (from-to)493-503
Number of pages11
JournalMonatshefte fur Mathematik
Volume197
Issue number3
DOIs
StatePublished - 1 Mar 2022

Keywords

  • Eberlein compact space
  • GO space
  • Monotonically normal space
  • Pseudocompact space
  • Subspace of ordinals
  • Δ-space

ASJC Scopus subject areas

  • Mathematics (all)

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