A note on monotonically metacompact spaces

Harold R. Bennett, Klaas Pieter Hart, David J. Lutzer

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

We show that any metacompact Moore space is monotonically metacompact and use that result to characterize monotone metacompactness in certain generalized ordered (GO) spaces. We show, for example, that a generalized ordered space with a σ-closed-discrete dense subset is metrizable if and only if it is monotonically (countably) metacompact, that a monotonically (countably) metacompact GO-space is hereditarily paracompact, and that a locally countably compact GO-space is metrizable if and only if it is monotonically (countably) metacompact. We give an example of a non-metrizable LOTS that is monotonically metacompact, thereby answering a question posed by S.G. Popvassilev. We also give consistent examples showing that if there is a Souslin line, then there is one Souslin line that is monotonically countable metacompact, and another Souslin line that is not monotonically countably metacompact.

Original languageEnglish
Pages (from-to)456-465
Number of pages10
JournalTopology and its Applications
Volume157
Issue number2
DOIs
StatePublished - Feb 1 2010

Keywords

  • Countably metacompact
  • GO-space
  • Generalized ordered space
  • LOTS
  • Metacompact
  • Metacompact Moore space
  • Metrizable
  • Monotonically countably metacompact
  • Monotonically metacompact
  • σ-Closed-discrete dense set

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