Topological Groupoids

A groupoid is a set G in which a single valued product ab is defined for every pair of elements a, b ε G. If G is a groupoid and at the same time a Hausdorff topological space, and, moreover, the multiplication in the groupoid G is continuous in the topological space G, then G is called a topological groupoid. Our aim in this dissertation is two-fold: (1) to study topological groupoids for their own sake; (2) to investigate the relation of certain topological properties to associativity. We note, in relation to the first motif, that many authors have dealt with non-associative algebraic structures, i.e. Albert [1]*, Frink [4], Garrison [5], Etherington [2], Hausmann and Ore [7], and Stein [22].