Introduction

Abstract

Groupoids are algebraic objects that behave like a group except that the multiplication operation is only partially defined. Topological groupoids provide a useful unifying model for groups and group actions, and equivalence relations induced by continuous maps between topological spaces. They also provide a good algebraic model for the quotient of a topological space by a group or semigroup action in instances where the quotient space itself is, topologically, poorly behaved { for example, the quotient of a shift-space determined by the shift map, or the quotient of the circle by an irrational rotation.