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Topologie der Polyeder und kombinatorische Topologie der Komplexe

Nature volume 143, pages 700701 (29 April 1939) | Download Citation



THE first systematic exposition of combinatory topology was made by Dehn and Heegaard in a section of the “Enzyklopadie der mathemat-ischen Wissenschaften”, in which the exact concepts involved are only developed as far as the third dimension. The extension of the theory to complexes of higher dimensions was fraught with considerable difficulties; and it was due to the work of M. A. H. Newman that the gap was finally bridged. In the section of the encyclopaedia referred to above, he showed that combinatory topology was one of the most primitive branches of geometry, in which the concept of limiting values had as yet no place. In fact, as Prof. Reidemeister describes in detail in the present treatise, combinatory topology turns out to be a well-defined partial domain of the theory of polyhedra—a fact well calculated to demonstrate the elementary character of the subject and to justify Prof. Reidemeister in providing a new and systematic presentation of it.

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