An internal characterisation of radiality

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Abstract

In this paper, we will investigate how radiality occurs in topological spaces by considering neighbourhood bases generated by nests. We will define a new subclass of radial spaces that contains LOTS, GO-spaces and spaces with well-ordered neighbourhood bases, called the independently-based spaces. We show that first-countable spaces are precisely the independently-based, strongly Fréchet spaces and we give an example of a Fréchet–Urysohn space that is neither independently-based nor strongly Fréchet.
Original languageEnglish
Pages (from-to)10-22
Number of pages13
JournalTopology and its Applications
Volume177
Early online date23 Aug 2014
DOIs
Publication statusPublished - 1 Nov 2014

Keywords

  • Fréchet–Urysohn
  • Independently-based
  • Nest
  • Nest system
  • Radial
  • Spoke
  • Spoke system
  • Strongly Fréchet
  • Well-based

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