Productivity of paracompactness in the class of the first-countable GO-spaces with certain dense subsets

P. Szewczak

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Let P be the class of all spaces whose Cartesian product with every paracompact space is paracompact. We prove that if X is a paracompact, first-countable GO-space with σDC dense subset then X∈P if and only if X is σDC. We also prove that if Y is a metric GO-space and X is a GO-space defined on Y then X is metrizable provided X∈P. These results support the validity of the Telgársky's conjecture which says that if X is a paracompact space then X∈P if and only if the first player of the G(DC, X) game introduced by R. Telgársky, see [13,4,5] has a winning strategy.

Original languageEnglish
Pages (from-to)39-49
Number of pages11
JournalTopology and its Applications
Volume165
Issue number1
DOIs
StatePublished - 15 Mar 2014
Externally publishedYes

Keywords

  • GO-spaces
  • Paracompactness
  • Productivity

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