Displaying similar documents to “Shape and strong shape equivalences”

Polyhedra with finite fundamental group dominate finitely many different homotopy types

Danuta Kołodziejczyk (2003)

Fundamenta Mathematicae

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In 1968 K. Borsuk asked: Does every polyhedron dominate only finitely many different shapes? In this question the notion of shape can be replaced by the notion of homotopy type. We showed earlier that the answer to the Borsuk question is no. However, in a previous paper we proved that every simply connected polyhedron dominates only finitely many different homotopy types (equivalently, shapes). Here we prove that the same is true for polyhedra with finite fundamental group.

Shape theory intrinsically.

Zvonko Cerin (1993)

Publicacions Matemàtiques

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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...