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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]] | ||
