闭图像定理
闭图像定理是数学中泛函分析的一条定理。
设
，
为巴拿赫空间，
为线性算子。定义
的图像为
的子空间
-
。
赋予范数
，使得成为巴拿赫空间。那么，这定理指是连续的（与有界等价）当且仅当
在内是闭集。
Closed graph theorem
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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.](/uploads/202501/05/Cubicpoly0828.png)
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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