Functional

A mapping $f$ of an arbitrary set $X$ into the set $\mathbb{R}$ of real numbers or the set $\mathbb{C}$ of complex numbers. If $X$ is endowed with the structure of a vector space, a topological space or an ordered set, then there arise the important classes of linear, continuous and monotone functionals, respectively (cf. Linear functional; Continuous functional; Monotone mapping).

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