About extension of homeomorphisms over zero-dimensional homogeneous spaces

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 → В to a homeomorphism f: X → X, where A and В are countable disjoint compact subsets of the space X. If, additionally, X is a nonpseudocompact space, then the homeomorphism g is extendable to a homeomorphism f: X→X\ A.