Monotone countable paracompactness

Chris Good, Robin Knight, Ian Stares

Research output: Contribution to journalArticlepeer-review

40 Citations (Scopus)

Abstract

We study a monotone version of countable paracompactness, MCP, and of countable metacompactness, MCM. These properties are common generalizations of countable compactness and stratifiability and are shown to relate closely to the generalized metric g-functions of Hodel: MCM spaces coincide with β-spaces and, for q-spaces (hence first countable spaces) MCP spaces coincide with wN-spaces. A number of obvious questions are answered, for example: there are "monotone Dowker spaces" (monotonically normal spaces that are not MCP); MCP, Moore spaces are metrizable; first countable (or locally compact or separable) MCP spaces are collectionwise Hausdorff (in fact we show that wN-spaces are collectionwise Hausdorff). The extent of an MCP space is shown to be no larger than the density and the stability of MCP and MCM under various topological operations is studied.

Original languageEnglish
Pages (from-to)281-298
Number of pages18
JournalTopology and its Applications
Volume101
Issue number3
Early online date29 Dec 1999
DOIs
Publication statusPublished - 3 Mar 2000

Keywords

  • β-space
  • Collectionwise Hausdorff
  • g-functions
  • MCM
  • MCP
  • Monotone countable metacompactness
  • Monotone countable paracompactness
  • Monotone Dowker space
  • Monotone normality
  • Moore space
  • Semi-stratifiability
  • Stratifiability
  • wN-space

ASJC Scopus subject areas

  • Geometry and Topology

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