A second countable locally compact transitive groupoid without open range map

Buneci, Mădălina

doi:10.1090/proc/14550

A second countable locally compact transitive groupoid without open range map
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by Mădălina Roxana Buneci PDF

Proc. Amer. Math. Soc. 147 (2019), 3603-3610 Request permission

Abstract:

Dana P. Williams raised in [Proc. Amer. Math. Soc., Ser. B 3 (2016), pp. 1–8] the following question: Must a second countable, locally compact, transitive groupoid have open range map? This paper gives a negative answer to that question. Although a second countable, locally compact transitive groupoid $G$ may fail to have open range map, we prove that we can replace its topology with a topology which is also second countable, locally compact, and with respect to which $G$ is a topological groupoid whose range map is open. Moreover, the two topologies generate the same Borel structure and coincide on the fibres of $G$.

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