Two theorems about relations
Hewitt Kenyon · Transactions of the American Mathematical Society · 1963
Introduction.The main result of this paper is Theorem 1 below, which is entirely relation-theoretic in character.It is applied to topological uniformities in the two corollaries^) which follow it, and it is in this connection that the theorem first came to my attention.Three counter-examples are given which show that certain reasonable-sounding improvements of Theorem 1 are impossible.Theorem 2 is included with this note because its subject matter is similar to that of Theorem 1.