Surveys in Mathematics and its Applications


ISSN 1842-6298 (electronic), 1843-7265 (print)
Volume 9 (2014), 55 -- 78

VARIOUS NOTIONS OF AMENABILITY FOR NOT NECESSARILY LOCALLY COMPACT GROUPOIDS

Mădălina Roxana Buneci

Abstract. We start with a groupoid G endowed with a family W of subsets mimicking the properties of a neighborhood basis of the unit space (of a topological groupoid with paracompact unit space). Using the family W we endow each G-space with a uniform structure. The uniformities of the G-spaces allow us to define various notions of amenability for the G-equivariant maps. As in [1], the amenability of the groupoid G is defined as the amenability of its range map. If the groupoid G is a group, all notions of amenability that we introduce coincide with the classical notion of amenability for topological (not necessarily locally-compact) groups.

2010 Mathematics Subject Classification: 22A22; 43A07; 54E15.
Keywords: groupoid; uniform structure; equivariant map; amenability.

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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