English

An internal characterisation of radiality

General Topology 2014-07-18 v2

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, called the independently-based spaces, that contains LOTS, GO-spaces and spaces with well-ordered neighbourhood bases. We show that first-countable spaces are precisely the independently-based, strongly Fr\'echet spaces and we give an example of a Fr\'echet-Urysohn space that is neither independently-based nor strongly Fr\'echet.

Cite

@article{arxiv.1401.6519,
  title  = {An internal characterisation of radiality},
  author = {Robert Leek},
  journal= {arXiv preprint arXiv:1401.6519},
  year   = {2014}
}

Comments

11 pages. Changelog: cleaned up LaTeX source and fixed 'folgenbestimmt' typo (thanks to Thilo Weinart for spotting this!)

R2 v1 2026-06-22T02:54:38.025Z