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Displaying similar documents to “Strong shape of the Stone-Čech compactification”

Function spaces and shape theories

Jerzy Dydak, Sławomir Nowak (2002)

Fundamenta Mathematicae

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The purpose of this paper is to provide a geometric explanation of strong shape theory and to give a fairly simple way of introducing the strong shape category formally. Generally speaking, it is useful to introduce a shape theory as a localization at some class of “equivalences”. We follow this principle and we extend the standard shape category Sh(HoTop) to Sh(pro-HoTop) by localizing pro-HoTop at shape equivalences. Similarly, we extend the strong shape category of Edwards-Hastings...

The Whitehead and the Smale theorems in shape theory

Jerzy Dydak

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CONTENTS§1. Introduction................................................................................................................................... 5§2. Some classes of objects and morphisms in pro-categories..................................................... 5§3. Shape category.................................................................................................................................... 14§4. Deformation dimension........................................................................................................................