Surveys in Mathematics and its Applications

ISSN1842-6298 (electronic), 1843-7265 (print)

Volume 12 (2017), 219 -- 227

This work is licensed under a Creative Commons Attribution 4.0 International License.## APPROXIMATIONS FOR UNIFORMLY CONTINUOUS FUNCTIONS ON GROUPOIDS

## 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.

## References

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University Constantin Brâncuşi,

Calea Eroilor No.30, 210135 Târgu-Jiu, Romania.

e-mail: ada@utgjiu.ro, mbuneci@yahoo.com

http://www.utgjiu.ro/math/mbuneci/