On Bicompact Extensions of Tychonoff Spaces.
On the dimension of increments of Tychonoff spaces
Trivial bundles and near-homeomorphisms
Extension properties of Stone-Čech coronas and proper absolute extensors
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...
Fixed-point free maps of Euclidean spaces
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
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