Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 5 (2010), 229 -- 245

UNIFORMLY CONTINUOUS FUNCTIONS ON NON-HAUSDORFF GROUPOIDS

Mădălina Roxana Buneci

Abstract. The purpose of this paper is to study the notion of uniform continuity introduced in [1]. For a locally compact (not necessarily Hausdorff) groupoid endowed with pre-Haar systems (in the sense of [1] adapted to non-Hausdorff case) we prove that the space of bounded compactly supported functions which are left and right uniformly continuous on fibres can be made into a *-algebra and endowed with a (reduced) C*-norm. The advantage of working with uniformly continuous on fibres functions is the fact that even if the groupoid does not admit a continuous Haar system, various C*-algebras can be associated with it.

2010 Mathematics Subject Classification: 22A22; 43A05; 46L05.
Keywords: Locally compact groupoid; Uniform continuity; Pre-Haar system; C*-algebra.

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\noindent Mădălina Buneci
University Constantin Brâncuşi,
Str. Geneva, Nr. 3, 210136 Târgu-Jiu, Romania.
e-mail: ada@utgjiu.ro
http://www.utgjiu.ro/math/mbuneci/

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