Maximum occurring at all points in a set

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Is there any term for "sets where maximum of a mathematical expression in attained"? I just want to know if the set has any specific name. The set is infinite (do not consider discrete points). The maximum is achieved in a subset of parameter space.

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In mathematics, the argument of the maximum (abbreviated arg max or argmax) is the set of points of the given argument for which the given function attains its maximum value.

From Wikipedia.

Notation-wise, it looks like $$E = \operatorname*{arg\,max}_{x\in \mathbb{R}} f(x)$$