On nerves of fine coverings of acyclic spaces

Umed H. Karimov (Author), Dušan Repovš (Author)

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 ▫$D^n$▫. (2) Every ▫$n$▫-dimensional cell-like compactum can be embedded into ▫$(2n+1)$▫-dimensional Euclidean space as a cellular subset. (3) There exists a locally compact planar set which is acyclic with respect to Čech homology and whose fine coverings are all nonacyclic.

Keywords

planar acyclic space;cellular compactum;absolute neighborhood retract;nerve;fine covering;embedding into Euclidean space;Čech homology;

Data

Language:	English
Year of publishing:	2015
Typology:	1.01 - Original Scientific Article
Organization:	UL FMF - Faculty of Mathematics and Physics
UDC:	515.164
COBISS:	16978521
ISSN:	1660-5446
Views:	433
Downloads:	361
Average score:	0 (0 votes)
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