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Abstract
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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.
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