CONTENTSIntroduction......................................................................................................................................... 5Chapter I Elementary topological characterizations of fundamental dimension........................... 6 1. Characterizations of fundamental dimension..................................................................... 6 2. The fundamental dimension of components of compacta.............................................. 9 3. The fundamental...
We show that one can reduce the study of global (in particular cohomological) properties of a compact Hausdorff space X to the study of its stable cohomotopy groups .
Any cohomology functor on the homotopy category of compact spaces factorizes via the stable shape category ShStab. This is the main reason why the language and technique of stable shape theory can be used to describe and analyze the global structure of compact spaces.
For a given Hausdorff compact space X, there exists a metric compact...
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 to sSh(pro-Top)...
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