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2013 | 11 | 11 | 1949-1959
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Skeletally Dugundji spaces

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EN
Abstrakty
EN
We introduce and investigate the class of skeletally Dugundji spaces as a skeletal analogue of Dugundji space. Our main result states that the following conditions are equivalent for a given space X: (i) X is skeletally Dugundji; (ii) every compactification of X is co-absolute to a Dugundji space; (iii) every C*-embedding of the absolute p(X) in another space is strongly π-regular; (iv) X has a multiplicative lattice in the sense of Shchepin [Shchepin E.V., Topology of limit spaces with uncountable inverse spectra, Uspekhi Mat. Nauk, 1976, 31(5), 191–226 (in Russian)] consisting of skeletal maps.
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
11
Strony
1949-1959
Opis fizyczny
Daty
wydano
2013-11-01
online
2013-08-23
Twórcy
autor
Bibliografia
  • [1] Arkhangel’skii A.V., A class of spaces which contains all metric and all locally compact spaces, Mat. Sb., 1965, 67(109)(1), 55–88 (in Russian)
  • [2] Bereznickiı Ju., On theory of absolutes, In: III Tiraspol Symposium on General Topology and its Applications, Tiraspol, August 20–28, 1973, Shtiinca, Kishinev, 1973, 13–15
  • [3] Chigogidze A., Inverse Spectra, North-Holland Math. Library, 53, North-Holland, Amsterdam, 1996
  • [4] Daniels P., Kunen K., Zhou H.X., On the open-open game, Fund. Math., 1994, 145(3), 205–220
  • [5] Hasumi M., A continuous selection theorem for extremally disconnected spaces, Math. Ann., 1969, 179, 83–89 http://dx.doi.org/10.1007/BF01350118
  • [6] Haydon R., On a problem of Pełczynski: Milutin spaces, Dugundji spaces and AE(0-dim), Studia Math., 1974, 52, 23–31
  • [7] Heindorf L., Shapiro L.B., Nearly Projective Boolean Algebras, Lecture Notes in Math., 1596, Springer, Berlin, 1994
  • [8] Kucharski A., Plewik Sz., Game approach to universally Kuratowski-Ulam spaces, Topology Appl., 2007, 154(2), 421–427 http://dx.doi.org/10.1016/j.topol.2006.05.007
  • [9] Kucharski A., Plewik Sz., Inverse systems and I-favorable spaces, Topology Appl., 2008, 156(1), 110–116 http://dx.doi.org/10.1016/j.topol.2007.12.016
  • [10] Kucharski A., Plewik Sz., Skeletal maps and I-favorable spaces, Acta Univ. Carolin. Math. Phys., 2010, 51(suppl.), 67–72
  • [11] Mioduszewski J., Rudolf L., H-Closed and Extremally Disconnected Hausdorff Spaces, Dissertationes Math. (Rozprawy Mat.), 66, Polish Academy of Sciences, Warsaw, 1969
  • [12] PeŁczynski A., Linear Extensions, Linear Averagings, and their Applications to Linear Topological Classification of Spaces of Continuous Functions, Dissertationes Math. (Rozprawy Mat.), 58, Polish Academy of Sciences, Warsaw, 1968
  • [13] Shapiro L.B., A counterexample in the theory of dyadic compacta, Uspekhi Mat. Nauk, 1985, 40(5), 267–268 (in Russian)
  • [14] Shapiro L.B., Spaces that are co-absolute to the generalized Cantor discontinuum, Dokl. Akad. Nauk SSSR, 1986, 288(6), 1322–1326 (in Russian)
  • [15] Shapiro L.B., On spaces that are coabsolute with dyadic compacta, Dokl. Acad. Nauk SSSR, 1987, 293(5), 1077–1081 (in Russian)
  • [16] Shchepin E.V., Topology of limit spaces with uncountable inverse spectra, Uspekhi Mat. Nauk, 1976, 31(5), 191–226 (in Russian)
  • [17] Shchepin E.V., Functors and uncountable degrees of compacta, Uspekhi Mat. Nauk, 1981, 36(3), 3–62 (in Russian)
  • [18] Shirokov L.V., External characterization of Dugundji spaces and kappa-metrizable compacta, Dokl. Akad. Nauk SSSR, 1982, 263(5), 1073–1077 (in Russian)
  • [19] Valov V.M., Some characterizations of the spaces with a lattice of d-open mappings, C. R. Acad. Bulgare Sci., 1986, 39(9), 9–12
  • [20] Valov V.M., Another characterization of AE(0)-spaces, Pacific J. Math., 1987, 127(1), 199–208 http://dx.doi.org/10.2140/pjm.1987.127.199
  • [21] Valov V., External characterization of I-favorable spaces, Math. Balkanica (N.S.), 2011, 25(1–2), 61–78
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0296-7
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