On Nerves of Fine Coverings of Acyclic Spaces

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• 作者：Umed H. Karimov ; Du?an Repov?
• 关键词：Primary 57N35 ; 57N60 ; Secondary 54C25 ; 54C56 ; 57N75 ; Planar acyclic space ; cellular compactum ; absolute neighborhood retract ; nerve ; fine covering ; embedding into Euclidean space ; ?ech homology
• 刊名：Mediterranean Journal of Mathematics
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：12
• 期：1
• 页码：205-217
• 全文大小：366 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1660-5454

文摘

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 ?ech homology and whose fine coverings are all nonacyclic.