Compactifying a convergence space with functions
type: Item
instance of: scholarly article
title: Compactifying a convergence space with functions
zbMATH Open document ID: 0855.54034
DOI: 10.1155/S0161171296000920
author: Robert P. André
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1996-09-30T00:00:00Z
full work available at URL: https://eudml.org/doc/47576
review text: Let \(f : X \to K\) be a continuous function from a noncompact Hausdorff convergence space \(X\) into a compact Hausdorff topological space \(K\). Let \(Y = \text{cl}_K f[X]\), \(K_X = \{F \subset X : F\) is compact\} and \(S(f) = \bigcap \{\text{cl}_Y f(X - F) : F \in K_X\} \subset K\). \(S(f)\) is a closed compact subset of \(Y\). The author introduces a convergence structure on \(X^f = X \cup S(f)\). The author proves that if \(X\) is LC, then \(X^f\) is a Hausdorff compactification of \(X\). He also shows that \(f\) has a continuous extension to \(X^f\). There are also several related interesting results.
Mathematics Subject Classification ID: 54D35
Mathematics Subject Classification ID: 54A20
Mathematics Subject Classification ID: 54B20
zbMATH DE Number: 930041
zbMATH Keywords: pretopological space
zbMATH Keywords: singular compactification
zbMATH Keywords: compact Hausdorff convergence space
zbMATH Keywords: convergence structure
zbMATH Keywords: Hausdorff compactification
reviewed by: S. Naimpally
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 930041