Last Updated
：2025/11/24
sequential continuity
Noun
uncountable
Japanese Meaning
関数が、収束する数列（xₙ → x）に対して、対応する数列 f(xₙ) が f(x) に収束する性質。 / 数学的解析において、数列の収束性を保持する連続性の概念。
Quizzes for review
(mathematical analysis) The property of a function f between metric spaces, that given a convergent sequence x_n→x*, then f(x_n)→f(x*), i.e. the property of a function that it preserves sequential convergence.
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sequential continuity
To verify the sequential continuity of a function f at a point x*, it suffices to show that whenever a sequence x_n converges to x*, the sequence f(x_n) converges to f(x*).
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To verify the sequential continuity of a function f at a point x*, it suffices to show that whenever a sequence x_n converges to x*, the sequence f(x_n) converges to f(x*).
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