Doctoral Dissertations
Date of Award
6-1959
Degree Type
Dissertation
Degree Name
Doctor of Philosophy
Major
Mathematics
Major Professor
Orville G. Harold
Committee Members
E. Cohen, Edward D. Harris, T. A. Fisher, D. D. Lillian, W. H. Flecther
Abstract
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].
Recommended Citation
Warne, Ronson J., "Topological Groupoids. " PhD diss., University of Tennessee, 1959.
https://trace.tennessee.edu/utk_graddiss/2968