Extending local homotopy equivalences
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We give an elementary proof of one of tom Dieck’s theorems. The theorem says that iff:X → Y is a local homotopy equivalence in a strong enough sense, thenf is a homotopy equivalence globally. Applications, 1. The base space of any numerable principalG-bundle is of the sme homotopy type as the Borel space of the bundle. 2. The nerve of a numerable coveringU ofX for which all finite intersections are contractible is of the same homotopy type asX.
KeywordsTopological Space Base Space Homotopy Type Homotopy Theory Formal Covering
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