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单词 SequentiallyContinuous
释义

sequentially continuous


Let X,Y be topological spacesMathworldPlanetmath. Then a f:XY is said to be sequentially continuous if for every convergent sequence xnx in X, f(xn)f(x) in Y.

Every continuous functionMathworldPlanetmathPlanetmath is sequentially continuous, however the converseMathworldPlanetmath is true only in first-countable spaces (for example in metric spaces).

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更新时间:2025/5/4 6:56:12