Skeletally Dugundji spaces

Andrzej Kucharski; Szymon Plewik; Vesko Valov

Open Mathematics (2013)

  • Volume: 11, Issue: 11, page 1949-1959
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Andrzej Kucharski, Szymon Plewik, and Vesko Valov. "Skeletally Dugundji spaces." Open Mathematics 11.11 (2013): 1949-1959. <http://eudml.org/doc/269203>.

@article{AndrzejKucharski2013,
abstract = {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.},
author = {Andrzej Kucharski, Szymon Plewik, Vesko Valov},
journal = {Open Mathematics},
keywords = {Absolute; Dugundji spaces; Inverse system; Open maps; Skeletally Dugundji spaces; Skeletal maps; open map; skeletal map; inverse system; Dugundji space; skeletally Dugundji space; absolute},
language = {eng},
number = {11},
pages = {1949-1959},
title = {Skeletally Dugundji spaces},
url = {http://eudml.org/doc/269203},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Andrzej Kucharski
AU - Szymon Plewik
AU - Vesko Valov
TI - Skeletally Dugundji spaces
JO - Open Mathematics
PY - 2013
VL - 11
IS - 11
SP - 1949
EP - 1959
AB - 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.
LA - eng
KW - Absolute; Dugundji spaces; Inverse system; Open maps; Skeletally Dugundji spaces; Skeletal maps; open map; skeletal map; inverse system; Dugundji space; skeletally Dugundji space; absolute
UR - http://eudml.org/doc/269203
ER -

References

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  10. [10] Kucharski A., Plewik Sz., Skeletal maps and I-favorable spaces, Acta Univ. Carolin. Math. Phys., 2010, 51(suppl.), 67–72 Zbl1228.54018
  11. [11] Mioduszewski J., Rudolf L., H-Closed and Extremally Disconnected Hausdorff Spaces, Dissertationes Math. (Rozprawy Mat.), 66, Polish Academy of Sciences, Warsaw, 1969 Zbl0204.22404
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  13. [13] Shapiro L.B., A counterexample in the theory of dyadic compacta, Uspekhi Mat. Nauk, 1985, 40(5), 267–268 (in Russian) 
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