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Paper   IPM / M / 16718
School of Mathematics
  Title:   Ellis semigroupoid
  Author(s):  Massoud Amini (Joint with F. Behrouzi)
  Status:   Published
  Journal: Semigroup Forum
  Vol.:  103
  Year:  2021
  Pages:   777-790
  Supported by:  IPM
We extend the notion of the enveloping semigroup of a locally compact group to the enveloping semigroupoid of a locally compact groupopid and show that there is a universal enveloping semigroupoid which is unique up to isomorphism. As in the group case, we associate the Ellis semigroupoid to an action of a locally compact groupoid on a fibrewise compact space. We define the notion of proximality for groupoid actions and characterize it in terms of Ellis semigroupoid.

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