The n-shape of compact pairs and weak proper n-homotopy

Yūji Akaike, Tsukuba, Japan

Keywords: the (n + 1)-dimensional universal Menger compactum, μ^{n+1}-manifold pair, Z-pair, n-shape, weak proper n-homotopy AMS Subject classification: 54C56, 55P55

Abstract: Let μ^{n+1} be the (n + 1)-dimensional universal Menger compactum and μ_{0}^{n+1} a Z-set in μ^{n+1} which homeomorphic to μ^{n+1}. We construct a categorical isomorphism from the n-shape category of Z-pairs in (μ^{n+1}, μ_{0}^{n+1}) to the weak proper n-homotopy category of complements of Z-pairs.