Regular Homeomorphisms of Finite Order on Countable Spaces

Abstract

Abstract.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 βG is the Stone–Čech compactification of G as a discrete semigroup, then for every idempotent p ∈ βG\﹛0﹜, the subset ﹛p,−p﹜ ⊂ βG generates algebraically the free product of one-element semigroups ﹛p﹜ and ﹛−p﹜.