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Displaying similar documents to “Local behavior and the Vietoris and Whitehead theorems in shape theory”

Strong shape theory

J. Dydak, J. Segal

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CONTENTS1. Introduction..................................................................................................................................... 52. Terminology and notation.................................................................................................................... 63. Proper maps on contractible telescopes.......................................................................................... 84. The strong shape category.....................................................................................................................

Shape theory of maps.

Zvonko Cerin (1995)

Revista Matemática de la Universidad Complutense de Madrid

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We shall describe a modification of homotopy theory of maps which we call shape theory of maps. This is accomplished by constructing the shape category of maps HMb. The category HMb is built using multi-valued functions. Its objects are maps of topological spaces while its morphisms are homotopy classes of collections of pairs of multi-valued functions which we call multi-binets. Various authors have previously given other descriptions of shape categories of maps. Our description is...