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COVERING HOMOTOPY THEOREMS AND UNIVERSAL
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1-l correspondence algebra arcwise connected bundle with fibre bundle with group chain complexes closed subgroup commutative diagram compact Hausdorff space compact open topology continuous map coordinate transformations covering homotopy theorem Definition denote DGR modules dimensional Eilenberg-MacLane space equivalence classes equivalence relation F defined f is continuous fibre bundles fibre F finite follows G-bundle graded R-module group G H restricted homeomorphism homology induces a map isomorphism KG(B last n-k Lemma Let f Let G locally compact locally compact Hausdorff locally connected M(n+k,k map f map H map of bundles map of coordinate matrix n-cells nbhds normal cell open covering principal bundle product bundle Proof pullback Q x G(n-l quaternions quotient space quotient space topology relative homeomorphism set of equivalence subcomplex subgroup of G subspace system of coordinate topological group trivial bundle tt X,x vector