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Consider the germs of continuous functions about some real number; say 0 for simplicity. Is there a nice way of quantifying the germs, in the sense of putting them into a bijection with a simpler set? I feel there should be a continuum of germs, but I'd be interested in something more explicit. Bonus points for constructing good representatives for the equivalence classes defining the germs, but I really doubt that's possible. Thanks.

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I'm afraid that there won't be any good answer. But germs of holomorphic functions on a complex manifold are easier to classify: power series. – Martin Brandenburg Jan 14 '13 at 13:57
And, for more or less the same reasons, germs of real analytic functions are classified by the power series. At any rate, the claim that there are continuum-many different germs is easy to show: there are continuum-many different constants, and there are only continuum-many continuous functions that are defined on an open interval around $0$, and there are only countably many open intervals we need to think about because we have a countable base of open sets. – Zhen Lin Jan 14 '13 at 14:39

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