On cell-like mappings and the dimensional full-valuedness of compacta
type: Item
instance of: scholarly article
title: On cell-like mappings and the dimensional full-valuedness of compacta
zbMATH Open document ID: 0890.54026
DOI: 10.1007/BF02309158
author: Yu. V. Lubenets
published in: Mathematical Notes
publication date: 1996-02-21T00:00:00Z
review text: In dimension theory examples are well known of dimensionally non-full-valued compacta, the dimension of the product of which being smaller than the sum of the dimensions of the factors. Recently, \textit{A. N. Dranishnikov} [Sov. Math., Dokl. 37, No. 3, 769-773 (1988); translation from Dokl. Akad. Nauk SSSR 300, No. 5, 1045-1049 (1988; Zbl 0669.54020)] constructed two four-dimensional ANR-compacta with semi-dimensional product, proving the existence of dimensionally non-full-valued ANR-compacta. Then \textit{V. L. Sukhikh} [Mosc. Univ. Math. Bull. 48, No. 2, 56-57 (1993); translation from Vestn. Mosk. Univ., Ser. I 48, No. 2, 104-106 (1993; Zbl 0809.54013)] has shown that any ANR-compactum can be represented in form of the cell-like image of a certain dimensionally full-valued ANR-compactum of the same dimension. The objective of this paper is to show that any compactum is the cell-like image of a dimensionally full-valued compactum with the same dimension. As dimensionally full-valued compacta we take \(\Delta\)-compacta, by which we mean compacta that can be represented in the form of the inverse limit of an inverse sequence of simplicial complexes and simplicial mappings [\textit{Y. Kodama}, Fundam. Math. 89, 13-22 (1975; Zbl 0314.55011)]. In addition, the proved theorem sharpens the theorem of \textit{R. D. Edwards} [\textit{J. J. Walsh}, Lect. Notes Math. 870, 105-118 (1981; Zbl 0474.55002)], using some constructions of the author [Russ. Math. Surv. 47, No. 4, 214-215 (1992); translation from Usp. Mat. Nauk 47, No. 4(286), 197-198 (1992; Zbl 0784.54036)].
Mathematics Subject Classification ID: 54E45
Mathematics Subject Classification ID: 55M10
Mathematics Subject Classification ID: 54F45
Mathematics Subject Classification ID: 54C55
Mathematics Subject Classification ID: 57N60
zbMATH DE Number: 846488
zbMATH Keywords: cell-like image
zbMATH Keywords: dimensionally full-valued compactum
MaRDI profile type: Publication
cites work: Q3822843
cites work: Dimensionally valuable cell-like resolution for \(ANR\)-compacta
cites work: On Δ-spaces and fundamental dimension in the sense of Borsuk
cites work: Q3928675
cites work: On a property of the fundamental dimension of UVn-mappings
full work available at URL: https://doi.org/10.1007/bf02309158
OpenAlex ID: W2078912208
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description: scientific article; zbMATH DE number 846488