The open-open topology for function spaces
type: Item
instance of: scholarly article
title: The open-open topology for function spaces
zbMATH Open document ID: 0807.54017
DOI: 10.1155/S0161171293000134
author: Kathryn F. Porter
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1993-03-15T00:00:00Z
full work available at URL: https://eudml.org/doc/47084
review text: Summary: Let \((X,T)\) and \((Y,T^*)\) be topological spaces and let \(F\subset Y^ X\). For each \(U\in T\), \(V\in T^*\), let \((U,V)= \{f\in F\): \(f(U)\subset V\}\). Define the set \(S_{oo}= \{(U,V)\): \(U\in T\) and \(V\in T^*\}\). Then \(S_{oo}\) is a subbasis for a topology, \(T_{oo}\) on \(F\), which is called the open-open topology. We compare \(T_{oo}\) with other topologies and discuss its properties. We also show that \(T_{oo}\), on \(H(X)\), the collection of all self-homeomorphisms on \(X\), is equivalent to the topology induced on \(H(X)\) by the Pervin quasi-uniformity on \(X\).
Mathematics Subject Classification ID: 54C35
Mathematics Subject Classification ID: 54H13
zbMATH DE Number: 130458
zbMATH Keywords: compact-open topology
zbMATH Keywords: admissible topology
zbMATH Keywords: Galois space
zbMATH Keywords: self- homeomorphism
zbMATH Keywords: quasi-uniform convergence
zbMATH Keywords: Pervin quasi-uniformity
MaRDI profile type: Publication
OpenAlex ID: W2006118152
description: scientific article; zbMATH DE number 130458