About Extension of Homeomorphisms over Zero-Dimensional Homogeneous Spaces
Authors
Sergey Vasiljevich Medvedev
South Ural State University
Keywords:
homogeneous space, homeomorphism, first axiom of countability, pseudocompact space
Abstract
Let X be a zero-dimensional homogeneous space satisfying the first axiom of countability. We prove the theorem about an extension of a homeomorphism g: A -> B to a homeomorphism f: X -> X, where A and B are countable disjoint compact subsets of the space X. If, additionally, X is a non-pseudocompact space, then the homeomorphism g is extendable to a homeomorphism f: X -> X \ A.
Author Biography
Sergey Vasiljevich Medvedev, South Ural State University
Cand.Sc. (Physics and Mathematics), Associate Professor, Mathematical and Functional Analysis Department
