Last Updated
：2025/11/26
lower semi-continuous
Adjective
not-comparable
of a real-valued function on a topological space
Japanese Meaning
ある位相空間上の実数値関数 f が、任意の実数 c に対して f⁻¹((−∞, c])（すなわち、関数値が c 以下となる点全体の集合）が閉集合となるとき、その関数は「下半連続」であると言う。
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 most that number is closed.
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lower semi-continuous
To guarantee the existence of a minimizer, we assume the energy functional is lower semi-continuous on the topological space.
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To guarantee the existence of a minimizer, we assume the energy functional is lower semi-continuous on the topological space.
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