Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
Volume 12 (2017), 219 -- 227

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Mădălina Roxana Buneci

Abstract. The purpose of this paper is to prove an approximation/extension theorem for a family of partial functions on a groupoid satisfying a uniform compatibility condition. In the particular case of a trivial groupoid G=X× X and a singleton family, we recover the well-known result of Katětov: every bounded uniformly continuous real-valued function f defined on a subspace of a uniform space X has a bounded uniformly continuous extension to X.

2010 Mathematics Subject Classification: 22A22; 54E15.
Keywords: groupoid, uniformity, extension theorem, approximation.

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Mădălina Buneci
University Constantin Brâncuşi,
Calea Eroilor No.30, 210135 Târgu-Jiu, Romania.