We characterize, in terms of X, the extensional dimension of the Stone-Čech corona βX∖X of a locally compact and Lindelöf space X. The non-Lindelöf case is also settled in terms of extending proper maps with values in , where L is a finite complex. Further, for a finite complex L, an uncountable cardinal τ and a -set X in the Tikhonov cube we find a necessary and sufficient condition, in terms of , for X to be in the class AE([L]). We also introduce a concept of a proper absolute extensor and characterize the product as the only locally compact and Lindelöf proper absolute extensor of weight τ > ω which has the same pseudocharacter at each point.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm222-2-3,
author = {A. Chigogidze},
title = {Extension properties of Stone-\v Cech coronas and proper absolute extensors},
journal = {Fundamenta Mathematicae},
volume = {220},
year = {2013},
pages = {155-173},
zbl = {1296.54021},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm222-2-3}
}
A. Chigogidze. Extension properties of Stone-Čech coronas and proper absolute extensors. Fundamenta Mathematicae, Tome 220 (2013) pp. 155-173. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm222-2-3/