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smooth_function [2013/09/13 20:34] nikolaj |
smooth_function [2014/03/21 11:11] 127.0.0.1 external edit |
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===== Smooth function ===== | ===== Smooth function ===== | ||
- | ==== Definition ==== | + | ==== Set ==== |
- | | @#88DDEE: $X,Y$ ... Banach spaces with topology | | + | | @#55CCEE: context | @#55CCEE: $X,Y$ ... Banach spaces with topology | |
- | | @#FFBB00: $f\in C^\infty(X,Y)$ | | + | | @#FFBB00: definiendum | @#FFBB00: $f\in C^\infty(X,Y)$ | |
- | | @#55EE55: $\forall (k\in \mathbb N).\ f\in C^k(X,Y)$ | | + | | @#55EE55: postulate | @#55EE55: $\forall (k\in \mathbb N).\ f\in C^k(X,Y)$ | |
- | | @#55EE55: $\lim_{k\to\infty}D^kf$ ... continuous | | + | | @#55EE55: postulate | @#55EE55: $\lim_{k\to\infty}D^kf$ ... continuous | |
==== Discussion ==== | ==== Discussion ==== | ||
=== Reference === | === Reference === | ||
Wikipedia: [[http://en.wikipedia.org/wiki/Differentiable_function|Differentiable function]], [[http://en.wikipedia.org/wiki/Smooth_function|Smooth function]] | Wikipedia: [[http://en.wikipedia.org/wiki/Differentiable_function|Differentiable function]], [[http://en.wikipedia.org/wiki/Smooth_function|Smooth function]] | ||
==== Parents ==== | ==== Parents ==== | ||
- | === Requirements === | + | === Context === |
[[Differentiable function]], [[Limit in a metric space]] | [[Differentiable function]], [[Limit in a metric space]] |