Spaces of densely continuous forms
type: Item
instance of: scholarly article
title: Spaces of densely continuous forms
zbMATH Open document ID: 0892.54009
DOI: 10.1023/A:1008666504767
author: S. T. Hammer
author: R. A. McCoy
published in: Set-Valued Analysis
publication date: 1998-03-11T00:00:00Z
review text: For each function \(f\) from a topological space \(X\) to a topological space \(Y\) with a dense set \(D\) of the points of continuity denote by \(\overline f\) the closure of \(f|_D\) in \(X\times Y\). Then \(\overline f\) is called a densely continuous form; it is a kind of multifunction from \(X\) to \(Y\). The paper studies mainly the topology of uniform convergence on compact sets on the space of densely continuous forms (which is denoted by \(D_k(X,Y))\), for locally compact spaces \(X\) and metric spaces \(Y\) having a metric satisfying the Heine-Borel property. Under these conditions on \(X\) and \(Y\) the complete metrizability, metrizability and first countability of \(D_k(X,Y)\) are equivalent to the condition that \(X\) is \(G\)-compact. Also necessary and sufficient conditions are given for a subset of \(D_k(X,Y)\) to be compact.
reviewed by: Ľubica Holá
Mathematics Subject Classification ID: 54C35
Mathematics Subject Classification ID: 54C60
zbMATH DE Number: 1127529
zbMATH Keywords: densely continuous form
zbMATH Keywords: topology of uniform convergence on compact sets
zbMATH Keywords: Heine-Borel property
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1127529