Provides the first counterexamples showing algebraic singular functions are not always dense in the ideal of C*-singular functions for certain étale non-Hausdorff groupoids, including a bundle of groups and one from a self-similar action.
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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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Algebraic singular functions are not always dense in the ideal of $C^*$-singular functions
Provides the first counterexamples showing algebraic singular functions are not always dense in the ideal of C*-singular functions for certain étale non-Hausdorff groupoids, including a bundle of groups and one from a self-similar action.
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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.