Circular orders admit convex uniform structures that describe their compactifications, yielding new results on G-compactifications and generalizations of Helly's selection theorem.
Sorin, The Roelcke Precompactness and Compactifications of Transformations Groups of Discrete Spaces and Homogeneous Chains, 2023, arXiv:2310.18570
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Graph and Ellis methods yield descriptions of Roelcke, Ellis, WAP, and graph compactifications for topological groups and enable study of remainder properties using Arhangelskii dichotomy theorems.
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Circular orders: topology and continuous actions
Circular orders admit convex uniform structures that describe their compactifications, yielding new results on G-compactifications and generalizations of Helly's selection theorem.
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On proper compactifications of topological groups
Graph and Ellis methods yield descriptions of Roelcke, Ellis, WAP, and graph compactifications for topological groups and enable study of remainder properties using Arhangelskii dichotomy theorems.