# Skeletally Dugundji spaces

Andrzej Kucharski; Szymon Plewik; Vesko Valov

Open Mathematics (2013)

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

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topAndrzej 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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