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A Urysohn type lemma for groupoids

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Madalina Roxana Buneci

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.

Keywords:
groupoid, Urysohn-type lemma, metrization theorem

2010 MSC:
22A22; 54E15, 54E35

*Theory and Applications of Categories,*
Vol. 32, 2017,
No. 28, pp 970-994.

Published 2017-08-02.

http://www.tac.mta.ca/tac/volumes/32/28/32-28.pdf

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