Hassler Whitney Collected Papers Volume I: Vol.1

ISBN-13: 9781461277408 / Angielski / Miękka / 2012 / 592 str.

James Eelles; Domingo Toledo

Opis

We present here the mathematical papers of Hassler Whitney. This collection contains all the published papers, with the exception of some short announcements that Whitney did not wish to be included. We also include the introduction to his book Geometric Integration Theory, and one previously unpublished manuscript on the four-color problem. The papers are presented under some broad categories: graphs- and combinatorics, differentiable functions and singularities, analytic spaces, manifolds, bundles and characteristic classes, topology and algebraic topology, geometric integration theory. Whitney intended to write an introduction to this collection. Unfortunately he left us no manuscript at the time of his death, May 10, 1989. We had discussed the possibility of using his paper "Moscow 1935 - Topology moving toward America," written for the Centennial of the American Mathematical Society, as part of his introduction to this collection, an idea which he much liked. We therefore include this paper, which contains personal information as well as mathematical reflections, as Whitney's own introduction to these volumes. Whitney's mathematical style, like his personal style, was that of an explorer and pioneer. One of the pictures included in these volumes shows him as a mountain climber. In mathematics, he preferred to work on undeveloped areas: break new ground and build foundations. During the last twenty years of his life he concentrated his efforts on developing an educational system that builds on the natural tendency in children to be explorers.

Spis treści

— Volume 1.- [82] Moscow 1935: Topology Moving Toward America.- 1 Graphs and Combinatorics.- [3] A theorem on graphs, Annals of Math. (2) v. 32, 1931,378–390.- [5] Non-separable and planar graphs, AMS Transac. v. 34, 1932, 339–362.- [6] Congruent graphs and the connectivity of graphs, Am. Jour. Math. v. 54, 1932, 150–168.- [10] The coloring of graphs, Annals of Math., (2) v. 33, 1932, 688–718.- [12] A set of topological invariants for graphs, Am. Jour. Math., v. 55, 1933, 231–235.- [13] On the classification of graphs, Am. Jour. Math., v. 55, 1933, 236–244.- [14] 2-Isomorphic graphs, Am. Jour. Math., v. 55, 1933, 245–254.- [17] Planar graphs, Fundamenta Math., V. 21, 1933, 73–84.- [23] On the abstract properties of linear dependence, Am. Jour. Math., v. 57, 1935, 509–533.- [37] A numerical equivalent of the four color problem, Monatshefte fur Math, un Phys. 3, 1937-207–213.- [77] On reducibility in the four color problem, unpublished manuscript, 1971.- [78] (With W. T. Tutte) Kempe chains and the four colour problem, Utilitas Mathematica 2(1972), 241–281.- 2 Differentiable Functions and Singularities.- [18] Analytic extensions of differentiable functions defined in closed sets, AMS Transac., v. 36, 1934, 63–89.- [19] Derivatives, difference quotients and Taylor’s formula, AMS Bull., v. 40, 1934, 89–94.- [20] Differentiable functions defined in closed sets I, AMS Transac., v. 36, 1934, 369–387.- [21] Derivatives, difference quotients and Taylor’s formula II, Annals of Math. (2) v. 35, 1934, 476–481.- [22] Functions differentiable on the boundaries of regions, Annals of Math. (2) v. 35, 1934, 482–485.- [26] A function not constant on a connected set of critical points, Duke Math. J., v. 1, 1935, 514–517.- [27] Differentiable functions defined in arbitrary subsets of Euclidean space, AMS Transac., v. 40, 1936, 309–317.- [45] Differentiability of the remainder term in Taylor’s formula, Duke Math. J., 10, 1943, 153–158.- [46] Differentiable even functions, Duke Math. J., 10, 1943, 159–160.- [47] The general type of singularity of a set of 2n ? 1 smooth functions of n variables, Duke Math. J., 10, 1943, 161–172.- [49] On the extension of differentiable functions, AMS Bull., 50, 1944, 76–81.- [55] On ideals of differentiable functions, Am. Jour. Math. 70, 1948, 635–658.- [61] On totally differentiable and smooth functions, Pacific J. Math. 1, 1951, 143–159.- [63] On singularities of mappings of Euclidean spaces, I. Mappings of the plane into the plane, Annals of Math. (2)62, 1955, 374–410.- [64] On functions with bounded n-th differences, J. de Maths. Pures et Appl. 36, 1957, 67–95.- [67] Singularities of mappings of Euclidean spaces, Symposium Internacional de Topologia Algebraica, Mexico, 1956, 285–301, Mexico, La Universidad Nacional Autonoma, 1958.- [70] On bounded functions with bounded n-th differences, AMS Proc. 10, 1959, 480–481.- 3 Analytic Spaces.- [66] Elementary structure of real algebraic varieties, Annals of Math. (2) 66, 1957, 545–556.- [68] (With F. Bruhat) Quelques propriétés fondamentales des ensembles analytiques-réels, Comm. Math. Helv. 33, 1959, 132–160.- [73] Local properties of analytic varieties, in: differential and combinatorial topology (Symposium in Honor of Marston Morse), Princeton, NJ, Princeton University Press, 1965, 205–244.- [74] Tangents to an analytic variety, Annals of Math (2) 81, 1965, 496–549.- Permissions.