Geodesic
Regular Homeomorphisms of Finite Order on Countable Spaces
Canadian journal of mathematics, Tome 61 (2009) no. 3, pp. 708-720

Voir la notice de l'article provenant de la source Cambridge University Press

We present a structure theorem for a broad class of homeomorphisms of finite order on countable zero dimensional spaces. As applications we show the following. (a) Every countable nondiscrete topological group not containing an open Boolean subgroup can be partitioned into infinitely many dense subsets. (b) If $G$ is a countably infinite Abelian group with finitely many elements of order 2 and $\beta G$ is the Stone–Čech compactification of $G$ as a discrete semigroup, then for every idempotent $p\,\,\in \,\,\beta G\backslash \{0\}$ , the subset $\{p,-p\}\subset \beta G$ generates algebraically the free product of one-element semigroups $\{p\}$ and $\{-p\}$ .
DOI : 10.4153/CJM-2009-038-x
Mots-clés : 22A30, 54H11, 20M15, 54A05, Homeomorphism, homogeneous space, topological group, resolvability, Stone–Čech compactification 
Zelenyuk, Yevhen. Regular Homeomorphisms of Finite Order on Countable Spaces. Canadian journal of mathematics, Tome 61 (2009) no. 3, pp. 708-720. doi: 10.4153/CJM-2009-038-x
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