engleski

The finite coarse shape - inverse systems approach and intrinsic approach

Given an arbitrary category C, a category pro*(f) -C is constructed such that the known pro-C category may be considered as a subcategory of pro*(f) -C and that pro*(f) -C may be considered as a subcategory of pro*-C. Analogously to the construction of the shape category Sh((C, D)) and the coarse category Sh((C, D))*, an (abstract) finite coarse shape category Sh((C, D))*f is obtained. Between these three categories appropriate faithful functors are defined. The finite coarse shape is also defined by an intrinsic approach using the notion of the epsilon-continuity. The isomorphism of the finite coarse shape categories obtained by these two approaches is constructed. Besides, an overview of some basic properties related to the notion of the epsilon-continuity is given.

Topological space ; metric space ; ANR ; category ; homotopy ; shape ; e-continuity

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