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 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 ; 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.
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