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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeOct 10th 2011

created placeholder for Hurewicz theorem

• CommentRowNumber2.
• CommentAuthorzskoda
• CommentTimeOct 10th 2011
• (edited Oct 10th 2011)

I have created several entries today, under construction, and will report more on that in few days, when having time, some are such stubs and some have some real material like Selberg integral.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeMay 22nd 2012
• (edited Aug 31st 2012)

noticed that Hurewicz theorem was still empty, and briefly added the statement

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeAug 31st 2012

added to Hurewicz theorem the definition of the Hurewicz homomorphism.

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeSep 22nd 2018

added paragraph (here) indicating the stable version and its generalization to the Boardman homomorphism

• CommentRowNumber6.
• CommentAuthorDmitri Pavlov
• CommentTimeMay 21st 2022

The original reference is

• Witold Hurewicz, _Beitrage zur Topologie der Deformationen), Neder. Akad. Wetensch. 38 (1935), 521–528.

The simplicial version is due to

• Daniel M. Kan, The Hurewicz theorem, 1958 Symposium internacional de topología algebraica (International symposium on algebraic topology), pp. 225–231 Universidad Nacional Autónoma de México and UNESCO, Mexico City.
• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeMay 21st 2022
• (edited May 21st 2022)

thanks. is there any online trace of Beiträge zur Topologie der Deformationen? I only see it listed on gbooks, where however no content is visible either

• CommentRowNumber8.
• CommentAuthorDmitri Pavlov
• CommentTimeMay 21st 2022

Re #7: The article is reproduced in its entirety in “Collected Works of Witold Hurewicz”, a book that is available online in Library Genesis.

Here is a full citation:

Koninklijke Akademie van Wetenschappen: Proceedings of the Section of Sciences 38 (1935), 112–119.

Mathematics. — Beiträge zur Topologie der Deformationen (l. Höherdimensionale Homotopiegruppen).

By Dr. W. Hurewicz

(Communicated by Prof. L. E. J. Brouwer).

• CommentRowNumber9.
• CommentAuthorUrs
• CommentTimeMay 22nd 2022

Right, I should have been more explicit: I am looking for useful hyperlinks that we could provide with the reference item on the nLab page. I guess we dont want to link to Library Genesis from nLab pages to avoid legal trouble.(?) At least thats what I used to not do.

• CommentRowNumber10.
• CommentAuthorUrs
• CommentTimeMay 22nd 2022

I noticed that the section stating the actual theorem (here) did not mention the cases in degree $\leq 1$. I have now filled that in by essentially copying over the two Propositions to this extent that we did have all along at singular homology.

Also added a kind of Idea-paragraph to before these statements (still here)

• CommentRowNumber11.
• CommentAuthorDmitri Pavlov
• CommentTimeMay 22nd 2022

• CommentRowNumber12.
• CommentAuthorDmitri Pavlov
• CommentTimeMay 22nd 2022
• (edited May 22nd 2022)

Re #9: I think supplying the book name is sufficient, which is what I just did. Everybody knows where to look for books these days. These Google Books links are now quite useless, by the way: it is virtually impossible to look inside. (This used to be quite different 10 years ago or so.)

• CommentRowNumber13.
• CommentAuthorUrs
• CommentTimeMay 22nd 2022

Okay, sounds good.

Sure, GoogleBooks rarely shows content these days, but in the absence of any published page for a reference, it is at least a kind of online proof of existence.

(Incidentally, some GBooks look inaccessible but do still open up as soon as one uses the “search inside” functionality. Not though in this case, unfortunately.)

• CommentRowNumber14.
• CommentAuthorDmitri Pavlov
• CommentTimeMay 23rd 2022

Added a direct link for the official digitized PDF of Hurewicz’s paper in the open digital archive of Indagationes Mathematicae.

• CommentRowNumber15.
• CommentAuthorUrs
• CommentTimeMay 23rd 2022

ah, great, thanks!

I have also updated the link here

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