Set-set topologies and semitopological groups
type: Item
instance of: scholarly article
title: Set-set topologies and semitopological groups
zbMATH Open document ID: 0681.54011
DOI: 10.1155/S0161171289000827
author: Kathryn F. Porter
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/46406
review text: Summary: Let G be a group with binary operation. Let T be a topology for G such that for all \(g\in G\) the maps, \(n_ g: G\to G\) and \({}_ gm: G\to G\), defined by \(m_ g(f)=f\cdot g\) and \({}_ gm(f)=g\cdot f\), respectively, are continuous. Then (G,T) is called a semitopological group. Some specific set-set topologies for function spaces are discussed and the concept of semitopologically determined collections of sets is introduced and used to classify some set-set topologies as semitopological groups.
Mathematics Subject Classification ID: 54C35
Mathematics Subject Classification ID: 57S05
Mathematics Subject Classification ID: 22A99
zbMATH DE Number: 4115508
zbMATH Keywords: point-open topology
zbMATH Keywords: compact-open topology
zbMATH Keywords: g-topology
zbMATH Keywords: B-topology
zbMATH Keywords: set- set topologies
zbMATH Keywords: semitopological groups
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4115508