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60A10-BorelMorphism.tex
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\documentclass[12pt]{article}
\usepackage{pmmeta}
\pmcanonicalname{BorelMorphism}
\pmcreated{2013-03-22 18:23:36}
\pmmodified{2013-03-22 18:23:36}
\pmowner{bci1}{20947}
\pmmodifier{bci1}{20947}
\pmtitle{Borel morphism}
\pmrecord{12}{41039}
\pmprivacy{1}
\pmauthor{bci1}{20947}
\pmtype{Definition}
\pmcomment{trigger rebuild}
\pmclassification{msc}{60A10}
\pmclassification{msc}{28A12}
\pmclassification{msc}{28C15}
\pmclassification{msc}{54H05}
\pmclassification{msc}{28A05}
%\pmkeywords{Borel morphism}
%\pmkeywords{Borel groupoids}
%\pmkeywords{left action of a groupoid on another}
\pmrelated{BorelSpace}
\pmrelated{Groupoids}
\pmrelated{CategoryOfBorelSpaces}
\pmrelated{MeasurableFunctions}
\pmrelated{BorelMeasure}
\pmdefines{algebraic morphism}
\endmetadata
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\begin{document}
\begin{definition}
Let $\grp_B$ and $\grp_B$* be two groupoids whose object spaces are Borel. An \emph{algebraic morphism} from $\grp_B$
to $\grp_B$* is defined as a left action of $\grp_B$ on $\grp_B$* which commutes with the multiplication on $\grp_B$. Such an algebraic morphism between Borel groupoids 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.,
\PMlinkexternal{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}
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\end{document}