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Tytuł artykułu

Locallyn-Connected Compacta and UV n-Maps

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We provide a machinery for transferring some properties of metrizable ANR-spaces to metrizable LCn-spaces. As a result, we show that for completely metrizable spaces the properties ALCn, LCn and WLCn coincide to each other. We also provide the following spectral characterizations of ALCn and celllike compacta: A compactum X is ALCn if and only if X is the limit space of a σ-complete inverse system S = {Xα , pβ α , α < β < τ} consisting of compact metrizable LCn-spaces Xα such that all bonding projections pβα, as a well all limit projections pα, are UVn-maps. A compactum X is a cell-like (resp., UVn) space if and only if X is the limit space of a σ-complete inverse system consisting of cell-like (resp., UVn) metrizable compacta.
Twórcy
autor
  • Department of Computer Science and Mathematics, Nipissing University, 100 College Drive, P.O. Box 5002, North Bay, ON, P1B 8L7, Canada
Bibliografia
  • [1] P. Bacon, Extending a complete metric, Amer. Math. Monthly 75 (1968) 642-643.
  • [2] S. Bogatyi and Ju. Smirnov, Approximation by polyhedra and factorization theorems for ANR-bicompacta. Fund. Math. 87 (1975), no. 3, 195–205 (in Russian).
  • [3] A. Chigogidze, Inverse spectra, North-Holland Math. Library 53 (Elsevier Sci. B.V., Amsterdam, 1996)
  • [4] A. Chigogidze, The theory of n-shapes, Russian Math. Surveys 44 (1989), 145–174.
  • [5] A. Dranishnikov, A private communication 1990.
  • [6] A. Dranishnikov, Universal Menger compacta and universal mappings, Math. USSR Sb. 57 (1987), no. 1, 131–149.
  • [7] A. Dranishnikov, Absolute ekstensors in dimension n and n-soft maps increasing dimension, UspekhiMat. Nauk 39 (1984), no. 5(239), 55–95 (in Russian).
  • [8] J. Dugundji, Modified Vietoris theorem for homotopy, Fund. Math. 66 (1970), 223–235.
  • [9] J. Dugundji and E. Michael, On local and uniformly local topological properties, Proc. Amer. Math. Soc. 7 (1956), 304–307.
  • [10] V. Gutev, Selections for quasi-l.sc. mappings with uniformly equi-LCn range, Set-Valued Anal. 1 (1993), no. 4, 319–328.
  • [11] S. Mardešic, On covering dimension and inverse limits of compact spaces, Illinois Math. Joourn. 4 (1960), no. 2, 278–291.
  • [12] N. To Nhu, Investigating the ANR-property of metric spaces, Fund. Math. 124 (1984), 243–254; Corrections: Fund. Math. 141 (1992), 297.
  • [13] S. T. Hu, Theory of retracts, Wayne State Univ. Press, Detroit, 1965.
  • [14] A. Karassev and V. Valov, Extension dimension and quasi-finite CW-complexes, Topology Appl. 153 (2006), 3241–3254. [WoS]
  • [15] B. Pasynkov, Monotonicity of dimension and open mappings that raise dimension, Trudy Mat. Inst. Steklova 247 (2004), 202–213 (in Russian).
  • [16] B. Pasynkov, On universal bicompacta of given weight and dimension, Dokl. Akad. Nauk SSSR 154 (1964), no. 5, 1042–1043 (in Russian).
  • [17] K. Sakai, Geometric aspects of general topology, Springer Monographs in Mathematics. Springer, Tokyo, 2013.
  • [18] E. Shchepin, Topology of limit spaces with uncountable inverse spectra, Uspekhi Mat. Nauk 31 (1976), no. 5(191), 191–226 (in Russian).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_agms-2015-0006
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