DISCOVERY OF THE "INVARIANCE OF DOMAIN"-THEOREM

BROUWER, L. E. J. [LUITZEN EGBERTUS JAN]. (+) DAVID HILBERT.

[Brouwer:] Beweis des ebenen Translationssatzes (+) Zur Invarianz des n-dimensionalen Gebiets (+) Beweis der Invarianz der geschlossene Kurve (+) [Hilbert:] Begründung der Kinetischen Gastheorie.

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)

Order-nr.: 44950