On nerves of fine coverings of acyclic spaces

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

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.

• Language: English
• Keywords: planar acyclic space, cellular compactum, absolute neighborhood retract, nerve, fine covering, embedding into Euclidean space, Čech homology
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2015
• Number of pages: Str. 205-217
• Numbering: Vol. 12, no. 1
• PID: 20.500.12556/RUL-111244
• UDC: 515.164
• ISSN on article: 1660-5446
• DOI: http://dx.doi.org/10.1007/s00009-014-0383-4
• COBISS.SI-ID: 16978521
• Publication date in RUL: 26.09.2019

Record is a part of a journal

• Title: Mediterranean journal of mathematics
• Shortened title: Mediterr. j. math.
• Publisher: Springer Nature, Birkhäuser
• ISSN: 1660-5446
• COBISS.SI-ID: 13561433