Date of Award
Doctor of Philosophy
Orville G. Harold
E. Cohen, Edward D. Harris, T. A. Fisher, D. D. Lillian, W. H. Flecther
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 *, Frink , Garrison , Etherington , Hausmann and Ore , and Stein .
Warne, Ronson J., "Topological Groupoids. " PhD diss., University of Tennessee, 1959.