Geodesic
About extension of homeomorphisms over zero-dimensional homogeneous spaces
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 5 (2013) no. 2, pp. 39-44

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Let $X$ be a zero-dimensional homogeneous space satisfying the first axiom of countability. We prove the theorem about an extension of a homeomorphism $g: A\to B$ to a homeomorphism $f: X\to X$, 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 $f: X\to X\setminus A$.
Keywords: homogeneous space; homeomorphism; first axiom of countability; pseudocompact space. 
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     author = {S. V. Medvedev},
     title = {About extension of homeomorphisms over zero-dimensional homogeneous spaces},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
     pages = {39--44},
     publisher = {mathdoc},
     volume = {5},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURM_2013_5_2_a4/}
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S. V. Medvedev. About extension of homeomorphisms over zero-dimensional homogeneous spaces. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 5 (2013) no. 2, pp. 39-44. http://geodesic.mathdoc.fr/item/VYURM_2013_5_2_a4/