Extension properties of Stone-Čech coronas and proper absolute extensors

• Autorzy: A. Chigogidze
• Języki publikacji: EN

Abstrakty

EN

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 $I^{τ}∖L$, where L is a finite complex. Further, for a finite complex L, an uncountable cardinal τ and a $Z_{τ}$-set X in the Tikhonov cube $I^{τ}$ we find a necessary and sufficient condition, in terms of $I^{τ}∖X$, for X to be in the class AE([L]). We also introduce a concept of a proper absolute extensor and characterize the product $[0,1) × I^{τ}$ as the only locally compact and Lindelöf proper absolute extensor of weight τ > ω which has the same pseudocharacter at each point.

Kategorie tematyczne

• 57N20: Topology of infinite-dimensional manifolds
• 54C20: Extension of maps
• 54D35: Extensions of spaces (compactifications, supercompactifications, completions, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2013
• Tom: 222
• Numer: 2
• Strony: 155-173

Daty

wydano

2013

Twórcy

autor

A. Chigogidze

• Department of Mathematics, College of Staten Island, CUNY, 2800 Victory Blvd., Staten Island, NY 10314, U.S.A.

Identyfikatory

DOI

10.4064/fm222-2-3