Topological Groupoid

A topological groupoid over $B$ is a Groupoid $G$ such that $B$ and $G$ are Topological Spaces and $\alpha$, $\beta$, and multiplication are continuous maps. Here, $\alpha$ and $\beta$ are maps from $G$ onto $\Bbb{R}^2$ with $\alpha:(x,\gamma,y)\mapsto x$ and $\beta:(x,\gamma,y)\mapsto y.$

References

Weinstein, A. ``Groupoids: Unifying Internal and External Symmetry.'' Not. Amer. Math. Soc. 43, 744-752, 1996.