Dyck's theorem in topology is sometimes stated as follows: the connected sum of a torus and projective plane is homeomorphic to the connected sum of three projective planes.

Certainly, this is the modern formulation of his theorem, given that Dyck proved his result in 1888 (the citation that I have seen for this theorem is usually given as: W. Dyck (1888), Beiträge zur Analysis situs. I. Math. Ann. 32, 457–512). For my own interest, I have been trying to read the original source of this theorem, but I'm having trouble mostly because Walther Dyck wrote in German whereas I am not fluent in the language. So, I was hoping to receive some help here.

Could someone explain to me how (and where) Dyck stated and proved his theorem in his 1888 Math. Ann. paper? This paper seems to be freely available at the following DOI: https://doi.org/10.1007/BF01443580. At over 50 pages long, I'm finding it quite a struggle to go through without any pointers, given my language barrier.

I am also curious whether this result also appeared earlier in any of his 3 papers published in Leipz. Ber. between 1885 and 1887 with the same title. The impression I have from the reviews on zbMATH Open is that the Math. Ann. papers expand upon the papers in Leipz. Ber., but I am not certain. I am also not able to locate the journal Leipz. Ber. anywhere, neither its full form nor its ISSN (if it has one), let alone the papers themselves.


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