A construction of Nöbeling manifolds of arbitrary weight

الأصل · EN

For each cardinal κ, each natural number n and each simplicial complex K we construct a space νⁿκ(K) and a map π νⁿκ(K) → K such that the following conditions are satisfied. 1. νⁿκ(K) is a complete metric n-dimensional space of weight κ. 2. νⁿκ(K) is an absolute neighborhood extensor in dimension n. 3. νⁿκ(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.