Contitunity on a Manifold

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AKG

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I wasn't using the Rn -> Rm notation as a substitute for M -> N. I was using it because it was what I thought you meant by the "basic definition from simple calculus". I only used Rn -> Rm to talk about the simple calculus definition of continuity, never the manifold definition. And the notation Rn -> Rm DOES mean that every point in Rn gets mapped to a point in Rm, just as M -> N means that every point in M gets mapped toa point in N.
 

matt grime

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Pete, a manifold is just some small chunks of R^n glued together via atlas on it. If you understand continuity in R^n, which is a totally local concept, you understand it on a manifold.
 
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matt grime said:
Pete, a manifold is just some small chunks of R^n glued together via atlas on it. If you understand continuity in R^n, which is a totally local concept, you understand it on a manifold.
I know what a manifold is. The reason for this thread/question was due to an error in the text I'm reading. The definition given in the text for continuity didn't seem right to me. But I believe that mathwonk posted a quote of that definition from the same text and its different than the one I used. The version he posted seems quite logical to me and thus makes sense. I think that we have texts from two different printings where mathwonk has a later printing with this correction in it.

Pete
 

mathwonk

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good to hear from you again pete. please forgive me for pushing the responses beyond the point where they were helpful.

best regards,

roy
 

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