A construction of Nöbeling manifolds of arbitrary weight

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