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Feb5-12, 05:22 PM
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Quote Quote by Identity View Post
Sorry, I've never heard of the term 'germ' before, can you explain please?
I assumed that by [itex]C^{\infty}(p)[/itex] you mean the set of real-valued functions f that are defined and smooth on some neighborhood U of p, modulo the equivalence relations according to which f~g iff f and g coincide on some small nbhd of p.

If so, then the elements of [itex]C^{\infty}(p)[/itex] are called germs of smooth functions.