Local $k$-connectedness of an inverse limit of polyhedra

Bell, G.; Nagórko, Andrzej

doi:10.4064/fm489-10-2019

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2020

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“…Local k-connectedness of inverse limits. The following theorem is proved in [6]. We cite it here for completeness.…”

Section: 5mentioning

confidence: 95%

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A construction of {N}

Bell

Nagórko

2020

Fund. Math.

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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.

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“…Local k-connectedness of inverse limits. The following theorem is proved in [6]. We cite it here for completeness.…”

Section: 5mentioning

confidence: 95%

“…(B(y, 1 n )) = 0 and by Lemma 5.3, f is a closed embedding. 6. Construction of Nöbeling manifolds of weight κ Construction 6.1.…”

mentioning

confidence: 99%