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nLab > Latest Changes: The Goursat theorem.

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    • CommentRowNumber1.
    • CommentAuthorTobyBartels
    • CommentTimeMar 11th 2012

    New stubs Édouard Goursat and Goursat theorem and some rearrangement of holomorphic function. I hope to put Goursat’s proof at Goursat theorem (but in the meantime you may see it PlanetMath) and consider its constructive content (probably assuming the fan theorem). But it might be a while before I get around to that.

    • CommentRowNumber2.
    • CommentAuthorColin Tan
    • CommentTimeApr 10th 2014

    Wrote a proof in synthetic differential geometry of the Cauchy integral formula from the Cauchy integral theorem.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeApr 10th 2014
    • (edited Apr 10th 2014)

    Thanks for writing this.

    Let’s see, this is about proving the Cauchy integral formula from the Cauchy integral theorem assuming that SDG may be applied.

    Now SDG may be applied if all functions are smooth. Goursat’s theorem specifically is advertized as being the proof of the statement assuming only that first derivatives exist.

    Therefore I would be inclined to put this proof instead into the entry Cauchy’s integral formula.

    What do you think?

    • CommentRowNumber4.
    • CommentAuthorColin Tan
    • CommentTimeApr 10th 2014
    I enjoyed reading Toby (I am guessing that Toby wrote it) outline the 5 step process of complex analyticity from complex differentiability. I agree with your suggestion, Urs, and have followed it. Thanks for creating the stub at Cauchy's integral formula.
    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeApr 10th 2014

    Okay, thanks again!

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