On nerves of fine coverings of acyclic spaces

Abstract

The main results of this paper are: (1) If a space $X$ can be embedded as a cellular subspace of ${\mathbb{R}}^n$ then $X$ admits arbitrary fine open coverings whose nerves are homeomorphic to the $n$-dimensional cube ${\mathbb{D}}^n$; (2) Every $n$-dimensional cell-like compactum can be embedded into $(2n+1)$-dimensional Euclidean space as a cellular subset; and (3) There exists a locally compact planar set which is acyclic with respect to Čech homology and whose fine coverings are all nonacyclic.

Cited by in corpus (1)

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