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"BROUWER, L. E. J. [LUITZEN EGBERTUS JAN]. (+) DAVID HILBERT.
Reference : 44950
(1912)
[Brouwer:] Beweis des ebenen Translationssatzes (+) Zur Invarianz des n-dimensionalen Gebiets (+) Beweis der Invarianz der geschlossene Kurve (+) [Hilbert:] Begründung der Kinetischen Gastheorie. - [DISCOVERY OF THE ""INVARIANCE OF DOMAIN""-THEOREM]
Leipzig, B.G. Teubner, 1912. 8vo. Bound in half cloth with the original printed wrappers. In ""Mathematische Annalen. Herausgegeben von A. Clebsch und C. Neumann. 68. Band. 3. Heft."" Entire issue offered.Black title-label in leather with gilt lettering to spine. Small library-label pasted on to top of spine. Small library stamp to title page and a few numbers written on front wrapper. Internally very fine and clean. [Brouwer:] Pp. 37-54" Pp. 55-6" Pp. 422-25 [Entire issue: (4), 595 pp.].
First printing of three important papers by Brouwer. In ""Zur Invarianz des n-dimensionalen Gebiets"" Brouwer introduced his ""Invariance of domain"" which is a theorem in topology about homeomorphic subsets of Euclidean space.""The existence of one-to-one correspondences between numerical spaces Rn for different n, shown by Cantor, together with Peano's subsequent example (1890) of a continuous mapping of the unit segment onto the square, had induced mathematicians to conjecture that topological mappings of numerical spaces Rn would preserve the number n (dimension). In 1910 Brouwer proved this conjecture for arbitrary n."" (DSB)
Beweis der Invarianz der Dimensionenzahl. - [THE FOUNDATION OF ALGEBRAIC TOPOLOGY]
Leipzig, B.G. Teubner, 1911. 8vo. Original printed wrappers, no backstrip and a small nick to front wrapper. In ""Mathematische Annalen. Begründet durch Alfred Clebsch und Carl Neumann. 70. Band. 2. Heft."" Entire issue offered. Internally very fine and clean. [Brouwer:] Pp. 161-65. [Entire issue: Pp. 161-296].
![Beweis der Invarianz der Dimensionenzahl. - [THE FOUNDATION OF ALGEBRAIC TOPOLOGY]. "BROUWER, L. E. J. [LUITZEN EGBERTUS JAN].](https://static.livre-rare-book.com/pictures/LLX/44532_1_thumb.jpg)
![Beweis der Invarianz der Dimensionenzahl. - [THE FOUNDATION OF ALGEBRAIC TOPOLOGY]. "BROUWER, L. E. J. [LUITZEN EGBERTUS JAN].](https://static.livre-rare-book.com/pictures/LLX/44532_2_thumb.jpg)
![Beweis der Invarianz der Dimensionenzahl. - [THE FOUNDATION OF ALGEBRAIC TOPOLOGY]. "BROUWER, L. E. J. [LUITZEN EGBERTUS JAN].](https://static.livre-rare-book.com/pictures/LLX/44532_3_thumb.jpg)
First printing of Brouwer's ""revolutionary"" and ""landmark"" contribution to topology. It marked a new period within topology-research: ""Although the paper is short and merely contains a simple proof of the invariance of dimension, ""it is infact much more than this - the paradigm of an entirely new and highly promising method now known as algebraic topology"""". (Aull. Handbook of the history of general topology. P. 150). ""The article submitted in June was the momentous ""Proof of the invariance of the dimension number"". In the following month it was followed with a longer paper, also a masterpiece. Of these two revolutionary papers, [The present paper] used his newly discovered ""degree of a mapping"" concept implicitly for the proof of dimensional invariance. [the paper] effectively swept away all previous attempts to prove dimensional invariance. (James. History of Topology, P. 16)""Cantor and others offered proofs that, indeed, a continuous mapping of points between dimensions was impossible, but a fully satisfactory proof establishing the invariance of dimension was not provided until the topologist L. E. J. Brouwer did so in 1910"". (DSB).
