Uniform Eberlein compactifications of metrizable spaces

Taras Banakh, Arkady Leiderman

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

We prove that each metrizable space X (of size |X|≤c) has a (first countable) uniform Eberlein compactification and each scattered metrizable space has a scattered hereditarily paracompact compactification. Each compact scattered hereditarily paracompact space is uniform Eberlein and belongs to the smallest class A of compact spaces, which contains the empty set, the singleton, and is closed under producing the Alexandroff compactification of the topological sum of a family of compacta from the class A.

Original languageEnglish
Pages (from-to)1691-1694
Number of pages4
JournalTopology and its Applications
Volume159
Issue number7
DOIs
StatePublished - 15 Apr 2012

Keywords

  • Hereditarily paracompact space
  • Metrizable space
  • Scattered compactification
  • Scattered space
  • Uniform Eberlein compact space

ASJC Scopus subject areas

  • Geometry and Topology

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