An internal characterisation of radiality

Robert Leek

doi:10.1016/j.topol.2014.08.002

An internal characterisation of radiality

Robert Leek

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

132 Downloads (Pure)

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 language	English
Pages (from-to)	10-22
Number of pages	13
Journal	Topology and its Applications
Volume	177
Early online date	23 Aug 2014
DOIs	https://doi.org/10.1016/j.topol.2014.08.002 https://doi.org/10.1016/j.topol.2014.08.002
Publication status	Published - 1 Nov 2014

Keywords

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

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LeekR2014InternalFinal published version, 344 KBLicence: Other (please provide link to licence statement

1 Citations
1 Doctoral Thesis
1 Working paper

Radiality and spokes: a structural theory of convergence
Leek, R., 15 Sept 2016, 194 p.
Research output: Thesis › Doctoral Thesis

Open Access
Convergence properties and compactifications
Leek, R., 15 May 2015, arXiv, p. 1, 12 p.
Research output: Working paper/Preprint › Working paper

Cite this

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title = "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 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 Fr{\'e}chet spaces and we give an example of a Fr{\'e}chet–Urysohn space that is neither independently-based nor strongly Fr{\'e}chet.",

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AB - 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.

KW - Fréchet–Urysohn

KW - Independently-based

KW - Nest

KW - Nest system

KW - Radial

KW - Spoke

KW - Spoke system

KW - Strongly Fréchet

KW - Well-based

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M3 - Article

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VL - 177

SP - 10

EP - 22

JO - Topology and its Applications

JF - Topology and its Applications

ER -

An internal characterisation of radiality

Abstract

Keywords

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Research output

Radiality and spokes: a structural theory of convergence

Convergence properties and compactifications

Cite this