حسن برسم

In this paper, we study topical functions f  X −→ K defined on a b-complete idempotent semimodule X over a b-complete idempotent semifield K with values in K Indeed, we characterize abstract concavity and support set of this class of functions. Next, we investigate abstract concavity of extended valued topical functions f  X −→ K, where K = K ∪  and  = sup K Finally, as an application by using extended valued elementary topical functions, we present characterizations of upward and downward sets.