Borel groupoid (original) (raw)

0.1 Definitions

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Definition 0.1.

A function fB:(X;ℬ)→(X;𝒞) of Borel spaces (http://planetmath.org/BorelSpace) is defined to be a Borel function if the inverse image of every Borel set under fB-1 is also a Borel set.

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  b. Borel groupoid

0.1.1 Analytic Borel space

𝔾B becomes an analytic groupoid (http://planetmath.org/LocallyCompactGroupoids) if its Borel structure isanalytic (http://planetmath.org/Analytic).

A Borel space (X;ℬ) is called analytic if it is countably separated, and also if it is the image of a Borel function from a standard Borel space.

References