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%%% Primary Title: Borel morphism
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%%% Filename: BorelMorphism.tex
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%%% Owner: bci1
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\begin{document}
\begin{definition}
Let $\grp_B$ and $\grp_B$* be two \htmladdnormallink{groupoids}{http://planetphysics.us/encyclopedia/QuantumOperatorAlgebra5.html} whose \htmladdnormallink{object}{http://planetphysics.us/encyclopedia/TrivialGroupoid.html} spaces are Borel. An \emph{\htmladdnormallink{algebraic}{http://planetphysics.us/encyclopedia/CoIntersections.html} \htmladdnormallink{morphism}{http://planetphysics.us/encyclopedia/TrivialGroupoid.html}} from $\grp_B$
to $\grp_B$* is defined as a left action of $\grp_B$ on $\grp_B$* which \htmladdnormallink{commutes}{http://planetphysics.us/encyclopedia/Commutator.html} with the multiplication on $\grp_B$. Such an algebraic morphism between \htmladdnormallink{Borel groupoids}{http://planetphysics.us/encyclopedia/BorelGroupoid.html} is said to be a \emph{Borel morphism} if the action of $\grp_B$ on $\grp_B$* is Borel (viz. ref. \cite{MRB2k6})
\end{definition}
\begin{thebibliography}{9}
\bibitem{MRB2k6}
M.R. Buneci. 2006.,
\htmladdnormallink{Groupoid C*-Algebras.}{http://www.utgjiu.ro/math/mbuneci/preprint/p0024.pdf},
{\em Surveys in Mathematics and its Applications}, Volume 1: 71--98.
\end{thebibliography}
\end{document}
