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bounded_function [2013/09/06 22:58] nikolaj created |
bounded_function [2013/09/06 23:03] nikolaj |
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| @#FFBB00: $f\in \text{BoundedFunction}(X)$ | | | @#FFBB00: $f\in \text{BoundedFunction}(X)$ | | ||
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- | | @#55EE55: $d:X\times X \to \mathbb{R}_+$ | | ||
| @#DDDDDD: $x,a\in X$ | | | @#DDDDDD: $x,a\in X$ | | ||
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==== Discussion ==== | ==== Discussion ==== | ||
+ | For linear operators between normed vector spaces, being bounded for each input element and continuous coincide. | ||
=== Reference === | === Reference === | ||
Wikipedia: [[http://en.wikipedia.org/wiki/Bounded_function|Bounded function]] | Wikipedia: [[http://en.wikipedia.org/wiki/Bounded_function|Bounded function]] |