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词汇 Closed graph theorem
分类 英语词汇 英语翻译词典
释义

Closed graph theorem

中文百科

闭图像定理

闭图像定理是数学中泛函分析的一条定理。

XY为巴拿赫空间,T:X \to Y为线性算子。定义T的图像为X \times Y的子空间

\Gamma (T) = \{(x,T(x))\in X\times Y \vert x \in X\}

赋予X \times Y范数\|(x,y) \|_{X\times Y} = \|x \|_X + \| y \|_Y,使得X \times Y成为巴拿赫空间。那么,这定理指T是连续的(与有界等价)当且仅当\Gamma (T) X \times Y内是闭集。

英语百科

Closed graph theorem 闭图像定理

The graph of the cubic function f(x) = x3 − 9x on the interval [-4,4] is closed because the function is continuous. The graph of the Heaviside function from [-2,2] is not closed, because the function is not continuous.
The Heaviside function

In mathematics, the closed graph theorem is a basic result which characterizes continuous functions in terms of their graphs. There are several versions of the theorem.

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