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A second countable locally compact transitive groupoid without open range map


Author: Mădălina Roxana Buneci
Journal: Proc. Amer. Math. Soc. 147 (2019), 3603-3610
MSC (2010): Primary 22A22; Secondary 54E15, 46H35
DOI: https://doi.org/10.1090/proc/14550
Published electronically: May 9, 2019
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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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Additional Information

Mădălina Roxana Buneci
Affiliation: University Constantin Brâncuşi of Târgu-Jiu, Calea Eroilor No. 30, 210135 Târgu-Jiu, România
Email: mbuneci@yahoo.com

DOI: https://doi.org/10.1090/proc/14550
Keywords: Transitive groupoid, principal groupoid, locally compact groupoid, range map
Received by editor(s): November 6, 2018
Published electronically: May 9, 2019
Communicated by: Adrian Ioana
Article copyright: © Copyright 2019 American Mathematical Society