A left topological monoid associated to a topological groupoid

2013/10/27 by Habib Amiri, Amiri, Habib
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1310.7222

openalex publication_date 2013/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper presents a fanctor S from the category of groupoids to the category of semigroups. Indeed, a monoid S_G with a right zero element is related to a topological groupoid G. The monoid S_G is a subset of C(G,G), the set of all continuous functions from G to G, and with the compact- open topology inherited from C(G,G) is a left topological monoid. The group of units of S_G, which is denoted by H(1), is isomorphic to a subgroup of the group of all bijection map from G to G under composition of functions. Moreover, it is proved that H(1) is embedded in the group of all invertible linear operators on C(G), the set of all complex continuous function on G.

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