Infinite deficiency in Menger manifolds

Yutaka Iwamoto, Tsukuba, Japan

AMS Subject classification: 54C55, 54F35

Keywords: Menger manifold, (n − 1)-homotopy, (n − 1)-homotopy kernel, μ_{∞}^{n}-manifold

Abstract: We introduce a new tool for describing Menger manifolds called μ^{n}-coordinate systems. Using μ^{n}-coordinate systems, we define the infinite deficiency for a subset of a μ^{n}-manifold and characterize Z-sets in terms of infinite deficiency. Moreover, we define the Δ_{n}-product of Menger manifolds and prove the stability theorem for the Δ_{n}-product.