Morphisms which are continuous on a neighborhood of the base of a groupoid

Details Morphisms which are continuous on a neighborhood of the base of a groupoid Morphisms which are continuous on a neighborhood of the base of a groupoid

2005-11-26

arxiv.org/abs/math/0511639v1

Studia Sci. Math. Hungar. 42(3) (2005), 281-292

Mathematics

Category Theory

11 pages

Scientific paper

Kirill Mackenzie raised the following question: given a groupoid morphism $F$ which is continuous on a neighborhood of base, is it true that $F$ is continuous everywhere? This paper gives a negative answer to that question. Moreover, we prove that for a locally compact groupoid $G$ with non-singleton orbits and having open target projection, if we assume that the continuity of every morphism $F$ on the neighborhood of the base in $G$ implies the continuity of $F$ everywhere, then the groupoid $G$ must be locally transitive.

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