Selecta Mathematica

by Menger, Karl

• ISBN13: 9783211837344
• ISBN10: 3211837345
• Edition: Bilingual
• Format: Hardcover
• Copyright: 2002-05-01
• Publisher: Springer Verlag

Summary

Karl Menger, one of the founders of dimension theory, belongs to the most original mathematicians and thinkers of the twentieth century. He was a member of the Vienna Circle and the founder of its mathematical equivalent, the Viennese Mathematical Colloquium. Both during his early years in Vienna and after his emigration to the United States, Karl Menger made significant contributions to a wide variety of mathematical fields, and greatly influenced some of his colleagues. The 'œSelecta Mathematica' contain Menger's major mathematical papers, based on a personal selection by himself out of his extensive writings. They deal with topics as diverse as topology, geometry, analysis and algebra, as well as writings on economics, sociology, logic, philosophy and mathematical results. The two volumes are a monument to the diversity and originality of Menger's ideas.

Table of Contents

Introduction	1	(6)
Schweizer, B.
Karl Menger and Vienna's Golden Autumn	7	(16)
Sigmund, K.
Commentary on Menger's Work on Dimension Theory	23	(10)
Johnson, D. M.
Selected Papers on Dimension Theory	33	(120)
Zur Dimensions- und Kurventheorie. Unveroffentlichte Aufsatze aus den Jahren 1921-1923, Monatshefte fur Mathematik und Physik 36 (1929), 411-432	35	(22)
Das Hauptproblem uber die dimensionelle Struktur der Raume, Proceedings Amsterdam 30 (1927), 138-144	57	(8)
(With W. Hurewicz). Dimension und Zusammenhangsstufe, Mathematische Annalen 100 (1928), 618-633	65	(16)
Allgemeine Raume und Cartesische Raume. I., Proceedings Amsterdam 29 (1926), 476-482	81	(8)
Allgemeine Raume und Cartesische Raume. II.: Uber umfassendste n-dimensionale Mengen, Proceedings Amsterdam 29 (1926), 1125-1128	89	(4)
Uber die Dimension von Punktmengen III. Zur Begrundung einer axiomatischen Theorie der Dimension Monatshefte fur Mathematik und Physik 36 (1929),193-218	93	(26)
Axiomatische Einfuhrung des Dimensionsbegriffes, Comptes Rendus du Premier Congres des Mathematiciens des Pays Slaves. Warszawa. 1929, 57-65	119	(10)
(With C. Kuratowski). Remarques sur la theorie axiomatique de la dimension, Monatshefte fur Mathematik und Physik 37 (1930), 169-174	129	(6)
Uber die Hinweise auf Brouwer in Urysohns Memoire, Selbstverlag, Wien 1932	135	(6)
Commentary on Menger's Work on Curve Theory and Topology	141	(12)
Crilly, T.
Moran, A.
Selected Papers on Curve Theory and Topology	153	(82)
Einige Uberdeckungssatze der Punktmengenlehre, Akademie der Wissenschaften zu Wien, Sitzungsberichte 133 (1924), 421-444	155	(24)
Grundzuge einer Theorie der Kurven, Mathematische Annalen 95 (1925), 277-306	179	(30)
Grundzuge einer Theorie der Kurven, Proceedings Amsterdam 28 (1925), 67-71	209	(6)
Une forme abstraite du theoreme de Borel-Lebesgue generalise, Comptes Rendus Acad. Paris 206 (1938), 563-565	215	(4)
On the Origin of the n-Arc Theorem, Journal of Graph Theory 5 (1981), 341-350	219	(10)
Commentary on Menger's ``Untersuchungen uber allgemeine Metrik''	229	(6)
Plaumann, P.
Strambach, K.
``Untersuchungen uber allgemeine Metrik''	235	(142)
Untersuchungen uber allgemeine Metrik (Erste Untersuchung: Theorie der Konvexitat; Zweite Untersuchung: Die euklidische Metrik; Dritte Untersuchung: Entwurf einer Theorie der n-dimensionalen Metrik), Mathematische Annalen 100 (1928), 75-163	237	(90)
Bemerkungen zur zweiten Untersuchung uber allgemeine Metrik, Proceedings Amsterdam 30 (1927), 710-714	327	(6)
Untersuchungen uber allgemeine Metrik. Teil IV: Zur Metrik der Kurven, Mathematische Annalen 103 (1930), 466-501	333	(36)
Commentary on Menger's Work on the Calculus of Variation and Metric Geometry	369	(8)
Sagan, H.
Selected Papers on Calculus of Variations	377	(40)
Sur un theoreme general du calcul des variations, Comptes Rendus Acad. Paris 201 (1935), 705-707	379	(4)
Calcul des variations dans les espaces distancies generaux, Comptes Rendus Acad. Paris 202 (1936), 1007-1009	383	(4)
Courbes minimisantes non rectifiables et champs generaux de courbes admissibles dans le calcul des variations, Comptes Rendus Acad. Paris 202 (1936), 1648-1650	387	(4)
Metric Methods in Calculus of Variations, Proc. Nat. Acad. Sci. 23 (1937), 244-250	391	(8)
A Theory of Length and its Applications to the Calculus of Variations, Proc. Nat. Acad. Sci. 25 (1939), 474-478	399	(6)
Commentary on Menger's Work on the Algebra of Geometry	405	(12)
Benz, W.
Selected Papers on Algebra of Geometry	417	(98)
Bemerkungen zu Grundlagenfragen. IV: Axiomatik der endlichen Mengen und der elementargeometrischen Verknupfungsbeziehungen, Jahresbericht der Deutschen Mathematikervereinigung 37 (1928), 309-325	419	(18)
(With F. Alt and O. Schreiber). New Foundations of Projective and Affine Geometry. Algebra of Geometry, Annals of Mathematics, II. Ser. 37 (1936), 456-482	437	(28)
(With F Alt). A Note on a Previous Paper ``New Foundations of Projective and Affine Geometry'', Annals of Mathematics, II. Ser. 38 (1937), 450	465	(2)
A New Foundation of Non-Euclidean, Affine, Real Projective and Euclidean Geometry, Proc. Nat. Acad. Sci. 24 (1938), 486-490	467	(6)
Self-Dual Fragments of the Ordinary Plane, The American Mathematical Monthly 56 (1949), 545-546	473	(2)
The Projective Space, Duke Math. Journal 17 (1950), 1-14	475	(14)
Frammenti piani autoduali e relative sostituzioni, Rendiconti Accad. Nazionale di Lincei 30 (1961 ), 713-717	489	(6)
The New Foundation of Hyperbolic Geometry, in: A Spectrum of Mathematics (Essays Presented to H. G. Forder), ed. by J. C. Butcher, Auckland University Press 1971, 86-97	495	(12)
Commentary on Menger's Expository Papers on Geometry	507	(8)
Benz W.
Selected Expository Papers on Geometry	515	(80)
Some Applications of Point-Set Methods, Annals of Mathematics, II. Ser. 32 (1931), 739-760	517	(22)
Generalized Vector Spaces. I. The Structure of Finite-Dimensional Spaces, Canadian Journal of Mathematics 1 (1949), 94-104	539	(12)
The Theory of Relativity and Geometry, in: Albert Einstein, Philosopher-Scientist, The Library of Living Philosophers, vol. VII, ed. by P. A. Schilpp, Evanston, Illinois 1949, 459-474	551	(16)
The Formative Years of Abraham Wald and His Work in Geometry, The Annals of Mathematical ' Statistics 23 (1952), 14-20	567	(8)
Mathematical Implications of Mach's Ideas: Positivistic Geometry The Clarification of Functional Connections, in: Ernst Mach, Physicist and Philosopher, Boston Studies in the Philosophy of Science VI, eds. R. S. Cohen and R. J. Seeger, D. Reidel, Dordrecht 1970, 107-125	575	(20)
List of Publications	595
Karl Menger