A second countable locally compact transitive groupoid without open range map
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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 $G$.References
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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
- Received by editor(s): November 6, 2018
- Published electronically: May 9, 2019
- Communicated by: Adrian Ioana
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 3603-3610
- MSC (2010): Primary 22A22; Secondary 54E15, 46H35
- DOI: https://doi.org/10.1090/proc/14550
- MathSciNet review: 3981137