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.

Title	Borel morphism
Canonical name	BorelMorphism
Date of creation	2013-03-22 18:23:36
Last modified on	2013-03-22 18:23:36
Owner	bci1 (20947)
Last modified by	bci1 (20947)
Numerical id	12
Author	bci1 (20947)
Entry type	Definition
Classification	msc 60A10
Classification	msc 28A12
Classification	msc 28C15
Classification	msc 54H05
Classification	msc 28A05
Related topic	BorelSpace
Related topic	Groupoids
Related topic	CategoryOfBorelSpaces
Related topic	MeasurableFunctions
Related topic	BorelMeasure
Defines	algebraic morphism