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:
“I care not by what measure you end the war. If you allow one single germ, one single seed of slavery to remain in the soil of America, whatever may be your object, depend upon it, as true as effect follows cause, that germ will spring up, that noxious weed will thrive, and again stifle the growth, wither the leaves, blast the flowers, and poison the fair fruits of freedom. Slavery and freedom cannot exist together.”
—Ernestine L. Rose (1810–1892)