English Dictionary

upper semi-continuous

形容詞

比較不可 位相空間論

(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.

日本語の意味

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。

On a compact topological space, any upper semi-continuous real-valued function attains its maximum.

コンパクトな位相空間上では、上半連続な実数値関数は必ず最大値を取る。

意味（1）

(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.

意味（2）

(of a real-valued function on a topological space) Such that for each fixed point x there is some neighborhood whose image's limit superior is x's image.