A simple proof that localic subgroups are closed
P. T. Johnstone (1988)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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P. T. Johnstone (1988)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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David Holgate (2000)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Christopher Townsend (2007)
Commentationes Mathematicae Universitatis Carolinae
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Given an axiomatic account of the category of locales the closed subgroup theorem is proved. The theorem is seen as a consequence of a categorical account of the Hofmann-Mislove theorem. The categorical account has an order dual providing a new result for locale theory: every compact subgroup is necessarily fitted.
Anders Kock, Ieke Moerdijk (1991)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Ieke Moerdijk (1990)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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L. Rudolf (1972)
Fundamenta Mathematicae
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Jean Pradines (2004)
Open Mathematics
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Starting with some motivating examples (classical atlases for a manifold, space of leaves of a foliation, group orbits), we propose to view a Lie groupoid as a generalized atlas for the “virtual structure” of its orbit space, the equivalence between atlases being here the smooth Morita equivalence. This “structure” keeps memory of the isotropy groups and of the smoothness as well. To take the smoothness into account, we claim that we can go very far by retaining just a few formal properties...