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].

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Mathematics Commons

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