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Regular Homeomorphisms of Finite Order on Countable Spaces

Published online by Cambridge University Press:  20 November 2018

Yevhen Zelenyuk
Yevhen Zelenyuk*
Affiliation:
School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, South Africa, yevhen.zelenyuk@wits.ac.za
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Abstract

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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.

  1. (a) Every countable nondiscrete topological group not containing an open Boolean subgroup can be partitioned into infinitely many dense subsets.

  2. (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 $\{-p\}$.

Keywords

22A3054H1120M1554A05Homeomorphismhomogeneous spacetopological groupresolvabilityStone–Čech compactification
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 61 , Issue 3 , 01 June 2009 , pp. 708 - 720
Copyright
Copyright © Canadian Mathematical Society2009

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