A construction of Nöbeling manifolds of arbitrary weight

G.~C. Bell, A. Nagórko Fundamenta Mathematicae MSC: Primary 55M10, 54F45; Secondary 54C55. DOI: 10.4064/fm488-10-2019 Published online: 1 April 2020

Abstract

For each cardinal $\kappa $, each natural number $n$, and each at most $n$-dimensional simplicial complex $K$ we construct a space ${\nu ^n_\kappa (K)}$ and a map $\pi \colon {\nu ^n_\kappa (K)} \to K$ such that the following conditions are satisfied:

(1) ${\nu ^n_\kappa (K)}$ is a complete $n$-dimensional metric space of weight $\kappa $;

(2) ${\nu ^n_\kappa (K)}$ is an absolute neighborhood extensor in dimension $n$;

(3) ${\nu ^n_\kappa (K)}$ is strongly universal in the class of complete $n$-dimensional metric spaces of weight $\kappa $; and

(4) $\pi $ is an $n$-homotopy equivalence.

For $\kappa = \omega $ 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.

Authors

  • G.~C. BellDepartment of Mathematics and Statistics
    University of North Carolina at Greensboro
    Greensboro, NC 27412, U.S.A.
    e-mail
  • A. NagórkoFaculty of Mathematics, Informatics, and Mechanics
    University of Warsaw
    Banacha 2
    02-097 Warszawa, Poland
    e-mail

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