On The Generalized Cauchy Equation

Abstract

It is the purpose of this note to prove the following theorem: Let ƒ: G → R be a non-constant continuous function with G a locally compact connected topological group and with R the real numbers. Let C = ƒ(G) and suppose that F: C × C → C is a junction such thatThen ƒ is monotone and open and F is continuous.