locally compact groupoids

1 Locally compact groupoids

This is a specific topic entry defining the basics of locally compact groupoidsPlanetmathPlanetmath and related concepts.

Let us first recall the related concepts of groupoidPlanetmathPlanetmathPlanetmathPlanetmath and topological groupoid, together with the appropriate notations needed to define a locally compact groupoid.

1.0.1 Groupoids and topological groupoids: categorical definitions

Recall that a groupoid 𝖦 is a small category with inversesMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath over its set of objects X=Ob(𝖦) . One writes 𝖦xy for the set of morphismsMathworldPlanetmathPlanetmath in 𝖦 from x to y .

A topological groupoid consists of a space 𝖦, a distinguished subspace 𝖦(0)=Ob(𝖦)𝖦, called the space of objects of 𝖦, together with maps

r,s: (1.1)