Difference between revisions of "Set of all derivations of a germ at a point"
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'''Note:''' not to be confused with: [[Set of all derivations at a point]] | '''Note:''' not to be confused with: [[Set of all derivations at a point]] | ||
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| + | '''Note:''' should have called this page "Set of all derivations of germs at a point" | ||
==Definition== | ==Definition== | ||
<math>\mathcal{D}_p(\mathbb{R}^n)</math><ref>Loring W. Tu - An introduction to manifolds - Second Edition</ref><ref>John M Lee - Introduction to smooth manifolds - second edition</ref> denotes the set of all [[Derivation|derivations]] of the form <math>D:C^\infty_p(\mathbb{R}^n)\rightarrow\mathbb{R}</math>, that is - it is a derivation of a set of [[Germ|germs]] - which is [[The set of all germs of smooth functions at a point]]. | <math>\mathcal{D}_p(\mathbb{R}^n)</math><ref>Loring W. Tu - An introduction to manifolds - Second Edition</ref><ref>John M Lee - Introduction to smooth manifolds - second edition</ref> denotes the set of all [[Derivation|derivations]] of the form <math>D:C^\infty_p(\mathbb{R}^n)\rightarrow\mathbb{R}</math>, that is - it is a derivation of a set of [[Germ|germs]] - which is [[The set of all germs of smooth functions at a point]]. | ||
Revision as of 23:48, 5 April 2015
Note: not to be confused with: Set of all derivations at a point
Note: should have called this page "Set of all derivations of germs at a point"
Definition
[math]\mathcal{D}_p(\mathbb{R}^n)[/math][1][2] denotes the set of all derivations of the form [math]D:C^\infty_p(\mathbb{R}^n)\rightarrow\mathbb{R}[/math], that is - it is a derivation of a set of germs - which is The set of all germs of smooth functions at a point.
