Uniformly continuous functions on non-Hausdorff groupoids
Journal Title: Surveys in Mathematics and its Applications - Year 2010, Vol 5, Issue 0
Abstract
The purpose of this paper is to study the notion of uniform continuity introduced in [M. Buneci, Haar systems and homomorphism on groupoids, Operator algebras and mathematical physics, 35-49, Theta, Bucharest, 2003]. For a locally compact (not necessarily Hausdorff) groupoid endowed with pre-Haar systems, 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<SUP>*</SUP>-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<SUP>*</SUP>-algebras can be associated with it.
Authors and Affiliations
Mădălina Buneci
Keywords
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