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I am looking for the original proof by Borsuk of the Borsuk-Ulam theorem. I would appreciate very much if someone could outline the proof.

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    $\begingroup$ Have you tried finding his paper? $\endgroup$
    – J.C. Ottem
    Commented Jan 16, 2012 at 8:49
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    $\begingroup$ Yeah, I tried various sources but could not find the original paper. $\endgroup$
    – kelly
    Commented Jan 16, 2012 at 9:50

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As J.C. Ottem suggests, the best thing in those cases is to look for the original paper. Wikipedia says

According to (Matoušek 2003, p. 25), the first historical mention of the statement of this theorem appears in (Lyusternik 1930). The first proof was given by (Borsuk 1933), where the formulation of the problem was attributed to Ulam.

Here (Borsuk 1933) is the paper

Drei Sätze über die n-dimensionale euklidische Sphäre, Fund. Math. 20: 177–190,

and a digitalized version of it can be found at this link.

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  • $\begingroup$ Many thanks for the paper. It was much needed. But, unfortunately, the paper is in german! Thanks anyway. $\endgroup$
    – kelly
    Commented Jan 16, 2012 at 9:53
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    $\begingroup$ Dann musst du ein W"orterbuch benutzen. $\endgroup$
    – Anthony Quas
    Commented Jan 16, 2012 at 16:33

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