An internal characterisation of radiality

作者：Leek Robert^*

来源：Topology and Its Applications, 2014, 177: 10-22.

DOI：10.1016/j.topol.2014.08.002

• Frechet-Urysohn
• Independently-based
• Nest
• Nest system
• Radial
• Spoke
• Spoke system
• Strongly Frechet
• Well-based

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

• 出版日期2014-11-1