Germ (mathematics) | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-10-07

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Germ_(mathematics)


00:00:37 1 Formal definition
00:00:56 1.1 Basic definition
00:01:53 1.2 More generally
00:02:31 1.3 Basic properties
00:03:09 2 Relation with sheaves
00:04:06 3 Examples
00:05:22 3.1 Notation
00:06:57 4 Applications
00:07:35 5 Algebraic properties
00:08:51 6 See also



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- Socrates


SUMMARY
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In mathematics, the notion of a germ of an object in/on a topological space is an equivalence class of that object and others of the same kind which captures their shared local properties. In particular, the objects in question are mostly functions (or maps) and subsets. In specific implementations of this idea, the sets or maps in question will have some property, such as being analytic or smooth, but in general this is not needed (the maps or functions in question need not even be continuous); it is however necessary that the space on/in which the object is defined is a topological space, in order that the word local have some sense.
The name is derived from cereal germ in a continuation of the sheaf metaphor, as a germ is (locally) the "heart" of a function, as it is for a grain.