Theory of Retracts

A₁ adjunction space ANR's arbitrarily given arbitrary point assume B₁ Banach space Borsuk canonical map Čech cohomology closed simplex closed subspace cohomology group compact metrizable space composed map contains convex COROLLARY countable Define a homotopy define a map deformation retract denote dimension disjoint Dugundji exists an open extension g extension of f f₁ finite number fixed-point property fully normal Fundam h₁ Hanner Hausdorff space Hence Hilbert cube homeomorphic homotopy ht identity map implies inclusion map integer K₁ LEMMA let f linear space locally connected locally finite locally finite open map defined map g map h Math metrizable space n-dimensional normal spaces open covering open neighborhood open refinement open set open subspace PROOF real number relative satisfying simplicial polytope star-refinement subpolytope subset taking THEOREM topological product U₁ V₁ vertices weakly hereditary Whitehead topology X₁ Y₁ λεΛ πη Φα