Abstract
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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The first author was partially supported by a grant from IPM (Grant No. 1400460121).
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Communicated by Jerome A. Goldstein.
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Amini, M., Behrouzi, F. Ellis semigroupoid. Semigroup Forum 103, 777–790 (2021). https://doi.org/10.1007/s00233-021-10206-w
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DOI: https://doi.org/10.1007/s00233-021-10206-w