Germ (mathematics)
In mathematics, the notion of a germ of an object in/on a topological space captures the local properties of the object. 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 specific properties, 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.
Read more about Germ (mathematics): Relation With Sheaves, Examples, Applications
Famous quotes containing the word germ:
“The germ of violence is laid bare in the child abuser by the sheer accident of his individual experience ... in a word, to a greater degree than we like to admit, we are all potential child abusers.”
—F. Gonzalez-Crussi, Mexican professor of pathology, author. “Reflections on Child Abuse,” Notes of an Anatomist (1985)