Last Updated
：2025/11/24
upper semi-continuous
Adjective
not-comparable
of a real-valued function on a topological space
Japanese Meaning
位相空間上の実値関数について、任意の実数を定数としたとき、その実数以上の値をとる点全体の集合が閉集合になるという性質を指す。
Sense（1）
Quizzes for review
(of a real-valued function on a topological space) Such that, for each fixed number, the subspace of points whose images are at least that number is closed.
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upper semi-continuous
On a compact topological space, any upper semi-continuous real-valued function attains its maximum.
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On a compact topological space, any upper semi-continuous real-valued function attains its maximum.
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