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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access August 23, 2013

Skeletally Dugundji spaces

  • Andrzej Kucharski EMAIL logo , Szymon Plewik and Vesko Valov
From the journal Open Mathematics

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.

MSC: 54C10; 54F65

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Published Online: 2013-8-23
Published in Print: 2013-11-1

© 2013 Versita Warsaw

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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