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Extension properties of Stone-Čech coronas and proper absolute extensors

100%

Chigogidze A.

Fundamenta Mathematicae

2013

tom 222

nr 2

155-173

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.

Fixed-point free maps of Euclidean spaces

63%

Buzyakova R., Chigogidze A.

Fundamenta Mathematicae

2011

tom 212

nr 1

1-16

Our main result states that every fixed-point free continuous self-map of ℝⁿ is colorable. This result can be reformulated as follows: A continuous map f: ℝⁿ → ℝⁿ is fixed-point free iff f̃: βℝⁿ → βℝⁿ is fixed-point free. We also obtain a generalization of this fact and present some examples

Ograniczanie wyników

2 Fundamenta Mathematicae

2 Chigogidze A.

1 Buzyakova R.

1 2013

1 2011

Wyniki wyszukiwania

Extension properties of Stone-Čech coronas and proper absolute extensors

Fixed-point free maps of Euclidean spaces