A Vietoris Mapping Theorem for Homotopy
نویسنده
چکیده
Let X and Y be compact metric spaces and let a map /: X—> Y be onto. The Vietoris Mapping Theorem as proved by Vietoris [8] states that if for all Ofkrfkn-1 and all yEY, flr(/_1(y)) =0 (augmented Vietoris homology mod two) then the induced homomorphism /*: Hr(X)-+Hr(Y) is an isomorphism onto for rfkn — l and onto for r=n. Begle [l; 2] has generalized this theorem to nonmetric spaces and more general coefficient groups. Simple examples show that an analogous theorem does not hold directly for homotopy. However by imposing strong local connectedness conditions, results can be obtained. That is the idea of this paper. We prove:
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تاریخ انتشار 2010