About Extension of Homeomorphisms over Zero-Dimensional Homogeneous Spaces

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