Generalizing Fung-Fu's theorem

Abstract

A connected order topological space, which is much simper than a real interval, is considered for the assignment problem of a rational aggregation by Fung and Fu, and they described the structure of an idempotent, commutative, associative, increasing and continuous binary operation on such a space. Fodor extended Fung-Fu's result to the non-commutative case. The aim of the present paper is to generalize Fodor's result to the non-idempotent case.