Borel morphism

Definition 0.1.

Let ${\\mathbb{G}}_{B}$ and ${\\mathbb{G}}_{B}$ * be two groupoids whose object spaces are Borel. An algebraic morphism from ${\\mathbb{G}}_{B}$ to ${\\mathbb{G}}_{B}$ * is defined as a left action of ${\\mathbb{G}}_{B}$ on ${\\mathbb{G}}_{B}$ * which commutes with the multiplication on ${\\mathbb{G}}_{B}$ . Such an algebraic morphism between Borel groupoids is said to be a Borel morphism if the action of ${\\mathbb{G}}_{B}$ on ${\\mathbb{G}}_{B}$ * is Borel (viz. ref. [1])

References

1 M.R. Buneci. 2006.,http://www.utgjiu.ro/math/mbuneci/preprint/p0024.pdfGroupoid C*-Algebras.,Surveys in Mathematics and its Applications, Volume 1: 71–98.

单词	BorelMorphism
释义	Borel morphism Definition 0.1. Let ${\\mathbb{G}}_{B}$ and ${\\mathbb{G}}_{B}$ * be two groupoids whose object spaces are Borel. An algebraic morphism from ${\\mathbb{G}}_{B}$ to ${\\mathbb{G}}_{B}$ * is defined as a left action of ${\\mathbb{G}}_{B}$ on ${\\mathbb{G}}_{B}$ * which commutes with the multiplication on ${\\mathbb{G}}_{B}$ . Such an algebraic morphism between Borel groupoids is said to be a Borel morphism if the action of ${\\mathbb{G}}_{B}$ on ${\\mathbb{G}}_{B}$ * is Borel (viz. ref. [1]) References 1 M.R. Buneci. 2006.,http://www.utgjiu.ro/math/mbuneci/preprint/p0024.pdfGroupoid C*-Algebras.,Surveys in Mathematics and its Applications, Volume 1: 71–98.
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