Rendiconti del Seminario Matematico della Università di Padova

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Volume 132, 2014, pp. 45–59
DOI: 10.4171/RSMUP/132-4

Almost periodic functions on groupoids

Farid Behrouzi[1]

(1) School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P. O. Box 19395-5746, 1993891176, Tehran, Iran

In this paper we generalize the notion of almost periodic functions on groups to the corresponding notion for groupoids. We prove a number of theorems about almost periodic functions in this general setting. We show that the set of almost periodic functions on a groupoid $ G , AP(G),$ is a C*-subalgebra of $ \ell ^{\infty }(G)$ . We investigate some topological properties of the maximal ideal space of $ AP(G) , {\mathfrak {b}}(G),$ and we obtain a continuous partial operation on ${\mathfrak {b}}G$ . Also, we study almost periodic functions on groupoids defined by an equivalence relation on a set $ X$ and obtain a compactification of $ X.$

Keywords: Groupoids, almost period function

Behrouzi Farid: Almost periodic functions on groupoids. Rend. Sem. Mat. Univ. Padova 132 (2014), 45-59. doi: 10.4171/RSMUP/132-4