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Shape theory intrinsically.

Zvonko Cerin (1993)

Publicacions Matemàtiques

We prove in this paper that the category HM whose objects are topological spaces and whose morphisms are homotopy classes of multi-nets is naturally equivalent to the shape theory Sh. The description of the category HM was given earlier in the article "Shape via multi-nets". We have shown there that HM is naturally equivalent to Sh only on a rather restricted class of spaces. This class includes all compact metric spaces where a similar intrinsic description of the shape category using multi-valued...

Shape theory of maps.

Zvonko Cerin (1995)

Revista Matemática de la Universidad Complutense de Madrid

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 intrinsic in...

Strong shape of the Stone-Čech compactification

Sibe Mardešić (1992)

Commentationes Mathematicae Universitatis Carolinae

J. Keesling has shown that for connected spaces X the natural inclusion e : X → β X of X in its Stone-Čech compactification is a shape equivalence if and only if X is pseudocompact. This paper establishes the analogous result for strong shape. Moreover, pseudocompact spaces are characterized as spaces which admit compact resolutions, which improves a result of I. Lončar.

Uniformly Movable Categories and Uniform Movability of Topological Spaces

P. S. Gevorgyan, I. Pop (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

A categorical generalization of the notion of movability from inverse systems and shape theory was given by the first author who defined the notion of movable category and used it to interpret the movability of topological spaces. In this paper the authors define the notion of uniformly movable category and prove that a topological space is uniformly movable in the sense of shape theory if and only if its comma category in the homotopy category HTop over the subcategory HPol of polyhedra is uniformly...

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