Function-space compactifications of function spaces
type: Item
instance of: scholarly article
title: Function-space compactifications of function spaces
zbMATH Open document ID: 1012.54023
DOI: 10.1016/S0166-8641(01)00089-X
published in: Topology and its Applications
publication date: 2002-08-22T00:00:00Z
review text: The paper presents a nice discussion of applications of the theory of continuous lattices in topology and analysis. We mention two pure topological results which are consequences of more general results: (1) If \(X\) and \(Y\) are compact Hausdorff spaces, then the space \(C_k(X,Y)\) of continuous mappings from \(X\) into \(Y\) with the compact-open topology can be embedded into the Vietoris hyperspace over \(X\times Y\) (by the graph mapping); (2) If \(X\) is a locally compact Hausdorff space, then the space \(C_k(X)\) of continuous real-valued functions on \(X\) with the compact open topology has a (Hausdorff) compactification by a space of pairs of semicontinuous extended real-valued mappings.
Mathematics Subject Classification ID: 54C35
Mathematics Subject Classification ID: 06B35
Mathematics Subject Classification ID: 54B35
Mathematics Subject Classification ID: 54B20
Mathematics Subject Classification ID: 54C30
zbMATH DE Number: 1787509
zbMATH Keywords: compactification
zbMATH Keywords: function spaces
zbMATH Keywords: Vietoris hyperspace
zbMATH Keywords: semicontinuous function
zbMATH Keywords: continuous lattice
zbMATH Keywords: Scott domain
zbMATH Keywords: Scott topology
zbMATH Keywords: dual topology
zbMATH Keywords: Lawson topology
zbMATH Keywords: Patch topology
zbMATH Keywords: compact-open topology
zbMATH Keywords: core-compact topology
zbMATH Keywords: Isbell topology
author: Martín Escardo
reviewed by: Ljubiša D. R. Kočinac
MaRDI profile type: Publication
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full work available at URL: s0166-8641(01)00089-x
OpenAlex ID: W2124181192
Wikidata QID: Q127373651
description: scientific article; zbMATH DE number 1787509