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Jul 24, 2018 at 20:00 comment added Duchamp Gérard H. E. Ramanan defines differential manifolds through sheaves (def 3.1. p12). I agree this is not focused to the question (condition (a) is explicitely that the topological space is second countable). However, this is a good place for this (rare) reference, thanks (+1)
Feb 12, 2012 at 14:28 comment added Martin Brandenburg @Sebastian: This point of view on manifolds was already mentioned in the "Background" section of the question. It does not answer the question.
Feb 10, 2012 at 7:59 comment added Daniel Moskovich How does that answer the question though? I don't think Ramanan addresses questions like this at all- his manifolds are explicitly Hausdorff second-countable, and the sheafs are explicitly sheafs of functions.
Feb 10, 2012 at 7:53 history answered Sebastian CC BY-SA 3.0