A construction of {N}

Abstract

For each cardinal κ, each natural number n and each simplicial complex K we construct a space ν n κ (K) and a map π : ν n κ (K) → K such that the following conditions are satisfied.(1) ν n κ (K) is a complete metric n-dimensional space of weight κ.(2) ν n κ (K) is an absolute neighborhood extensor in dimension n.(3) ν n κ (K) is strongly universal in the class of n-dimensional complete metric spaces of weight κ.(4) π is an n-homotopy equivalence. For κ = ω the constructed spaces are n-dimensional separable Nöbeling manifolds. The constructed spaces have very interesting fractal-like internal structure that allows for easy construction, subdivision, and surgery of brick partitions.