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On open maps and related functions over the Salbany compactification

Mbekezeli Nxumalo — 2024

Archivum Mathematicum

Given a topological space X , let 𝒰 X and η X : X 𝒰 X denote, respectively, the Salbany compactification of X and the compactification map called the Salbany map of X . For every continuous function f : X Y , there is a continuous function 𝒰 f : 𝒰 X 𝒰 Y , called the Salbany lift of f , satisfying ( 𝒰 f ) η X = η Y f . If a continuous function f : X Y has a stably compact codomain Y , then there is a Salbany extension F : 𝒰 X Y of f , not necessarily unique, such that F η X = f . In this paper, we give a condition on a space such that its Salbany map is open. In particular,...

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