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:
“And such the trust that still were mine,
Though stormy winds swept o’er the brine,
Or though the tempest’s fiery breath
Roused me from sleep to wreck and death.
In ocean cave, still safe with Thee
The germ of immortality!
And calm and peaceful shall I sleep,
Rocked in the cradle of the deep.”
—Emma Hart Willard (1787–1870)