An internal characterisation of radiality

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 Fréchet spaces and we give an example of a Fréchet-Urysohn space that is neither independently-based nor strongly Fréchet.

arXiv comment11 pages. Changelog: cleaned up LaTeX source and fixed 'folgenbestimmt' typo (thanks to Thilo Weinart for spotting this!)