germ (mathematics)

This article is about the mathematical notion of an equivalence class of functions. For the disease-causing organisms see Germ. For the Pre-Raphaelite journal entitled The Germ, see The Germ (periodical).

In mathematics, a germ is an equivalence class of continuous functions from one topological space to another (often from the real line to itself), in which one point x₀ in the domain has been singled out as privileged. Two functions f and g are equivalent precisely if there is some open neighborhood U of x₀ such that for all x ∈ U, the identity f(x) = g(x) holds. All local properties of f at x₀ depend only on which germ f belongs to. When the spaces are Riemann surfaces, germs can be viewed as power series, and thus the set of germs can be considered to be the analytic continuation of an analytic function. The article on Riemann surfaces provides additional detail on germs in this context. See also: Sheaf

<< Previous

Word Browser

Next >>

john ciardi
sogdian
alistair darling
olive higgins prouty
train routes in the netherlands
ohmynews
platon lebedev
bank menatep
jan carl raspe
special vfr
cisalpine republic

uncontrolled airspace
deep house
dme
fast, cheap and out of control
oscar kjellberg
reichsgau wartheland
radical republican
shahrukh khan
fallingwater
cooley tukey fft algorithm
andrew hill

laval university
feistel cipher
zoom lens
rational selfishness
georges dor
visual flight (airplanes)
oankali
international young democrat union
capital loss
michael feldman's whad'ya know?
aircraft attitude

andre borrel
glass harmonica
either
michael feldman
andrew rosindell
biometric word list
malcolm reed
akizuki tanezane
sakabato
amakazu kagemochi
amago clan