The Universal Minimal Space for Groups of Homeomorphisms of H-homogeneous Spaces
نویسنده
چکیده
Let X be a h-homogeneous zero-dimensional compact Hausdorff space, i.e. X is a Stone dual of a homogeneous Boolean algebra. It is shown that the universal minimal space M(G) of the topological group G = Homeo(X), is the space of maximal chains on X introduced in [Usp00]. If X is metrizable then clearly X is homeomorphic to the Cantor set and the result was already known (see [GW03]). However many new examples arise for non-metrizable spaces. These include, among others, the generalized Cantor sets X = {0, 1} for non-countable cardinals κ, and the corona or remainder of ω, X = βω \ ω, where βω denotes the Stone-Čech compactification of the natural numbers.
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