Extension properties of Stone-Čech coronas and proper absolute extensors

A. Chigogidze

Fundamenta Mathematicae (2013)

  • Volume: 222, Issue: 2, page 155-173
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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A. Chigogidze. "Extension properties of Stone-Čech coronas and proper absolute extensors." Fundamenta Mathematicae 222.2 (2013): 155-173. <http://eudml.org/doc/282710>.

@article{A2013,
abstract = {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.},
author = {A. Chigogidze},
journal = {Fundamenta Mathematicae},
keywords = {Stone-Čech corona; set; finite complex; absolute extensor},
language = {eng},
number = {2},
pages = {155-173},
title = {Extension properties of Stone-Čech coronas and proper absolute extensors},
url = {http://eudml.org/doc/282710},
volume = {222},
year = {2013},
}

TY - JOUR
AU - A. Chigogidze
TI - Extension properties of Stone-Čech coronas and proper absolute extensors
JO - Fundamenta Mathematicae
PY - 2013
VL - 222
IS - 2
SP - 155
EP - 173
AB - 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.
LA - eng
KW - Stone-Čech corona; set; finite complex; absolute extensor
UR - http://eudml.org/doc/282710
ER -

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