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arXiv · 1811.02692

A second countable locally compact transitive groupoid without open range map

Mădălina Roxana Buneci
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Abstract

Dana P. Williams raised in [Proc. Am. Math. Soc., Ser. B, 2016] 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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Mădălina Roxana Buneci. 2018-11-06. A second countable locally compact transitive groupoid without open range map. https://arxiv.org/abs/1811.02692

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