Geodesic
A Urysohn type lemma for groupoids
Theory and applications of categories, Tome 32 (2017), pp. 970-994

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Starting from the observation that through groupoids we can express in a unified way the notions of fundamental system of entourages of a uniform structure on a space X, respectively the system of neighborhoods of the unity of a topological group that determines its topology, we introduce in this paper a notion of G-uniformity for a groupoid G. The topology induced by a G-uniformity turns G into a topological locally transitive groupoid. We also prove a Urysohn type lemma for groupoids and obtain metrization theorems for groupoids unifying in two ways the Alexandroff-Urysohn Theorem and Birkhoff-Kakutani Theorem.

Publié le :
Classification : 22A22, 54E15, 54E35
Keywords: groupoid, Urysohn-type lemma, metrization theorem 
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     author = {Madalina Roxana Buneci},
     title = {A {Urysohn} type lemma for groupoids},
     journal = {Theory and applications of categories},
     pages = {970--994},
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     volume = {32},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2017_32_a27/}
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Madalina Roxana Buneci. A Urysohn type lemma for groupoids. Theory and applications of categories, Tome 32 (2017), pp. 970-994. http://geodesic.mathdoc.fr/item/TAC_2017_32_a27/