On biradial topological spaces and groups
type: Item
instance of: scholarly article
title: On biradial topological spaces and groups
zbMATH Open document ID: 0707.22001
DOI: 10.1016/0166-8641(90)90007-O
published in: Topology and its Applications
publication date: 1990-01-01T00:00:00Z
review text: A space X is called biradial if for every filter base \(\xi\) converging to \(x\in X\) there exists a chain \(\eta\) converging to x and meshing with \(\xi\) (i.e. for every \(A\in \eta\) and every \(B\in \xi\), \(A\cap B\neq \emptyset)\). The main attention of the paper is given to biradial topological groups. It is proved that: 1) If X is a regular biradial space, then for every \(x\in X\) there exists a chain \(\eta\) in X consisting of open sets and converging to x. 2) A topological group G is biradial iff there exists a chain \(\eta\) consisting of open sets which is a base for the space G at the point \(e\in G\). 3) A topological group G is metrizable iff G is biradial and the pseudocharacter of G is countable.
Mathematics Subject Classification ID: 22A05
Mathematics Subject Classification ID: 54A20
Mathematics Subject Classification ID: 54E20
Mathematics Subject Classification ID: 54D55
zbMATH DE Number: 4161006
zbMATH Keywords: free topological group
zbMATH Keywords: stratifiable
zbMATH Keywords: monotonically normal
zbMATH Keywords: \(\pi \) - nested
zbMATH Keywords: filter base
zbMATH Keywords: biradial topological groups
zbMATH Keywords: regular biradial space
zbMATH Keywords: chain
zbMATH Keywords: open sets
zbMATH Keywords: metrizable
zbMATH Keywords: pseudocharacter
author: A. V. Arhangel'skii
MaRDI profile type: Publication
cites work: RELATIONS AMONG THE INVARIANTS OF TOPOLOGICAL GROUPS AND THEIR SUBSPACES
cites work: Q3873152
cites work: Classes of topological groups
cites work: Q3767519
cites work: Q4150804
cites work: Q3218783
cites work: Q3469883
cites work: Quotienten geordneter Räume und Folgenkonvergenz
cites work: Q3753114
cites work: A quintuple quotient quest
cites work: Q5785710
full work available at URL: 0166-8641(90)90007-o
OpenAlex ID: W2146865182
description: scientific article; zbMATH DE number 4161006