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Group action on zero-dimensional spaces. (English) Zbl 1118.54011
For a Tychonoff space \(X\), a group topology on the group \(\mathcal H(X)\) of self-homeomorphisms is admissible provided that the evaluation map \(\mathcal H(X)\times X\to X\) is continuous. It is shown that if \(X\) is the product of a family of zero-dimensional spaces in which any two non-empty clopen subspaces of each factor are homeomorphic then the collection of admissible group topologies on \(X\) is a complete lattice. The minimum element is identified and is a familiar compactification in some cases.

54C35 Function spaces in general topology
57S05 Topological properties of groups of homeomorphisms or diffeomorphisms
54H99 Connections of general topology with other structures, applications
Full Text: DOI
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