Hassler Whitney Collected Papers Volume I: Vol.1 (Contemporary Mathematicians)

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 We also include the introduction to his book Geometric Integration Theory, and one previously unpublished manuscript on the four-color problem.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. Front Matter....Pages i-xiv Moscow 1935: Topology Moving Toward America....Pages 1-21 Front Matter....Pages 23-23 A Theorem on Graphs....Pages 24-36 Non-Separable and Planar Graphs....Pages 37-59 Congruent Graphs and the Connectivity of Graphs....Pages 61-79 The Coloring Of Graphs....Pages 80-110 A Set of Topological Invariants for Graphs....Pages 111-115 On the Classification of Graphs....Pages 116-124 2-Isomorphic Graphs....Pages 125-134 Planar Graphs....Pages 135-146 On the Abstract Properties of Linear Dependence....Pages 147-171 A numerical equivalent of the four color map Problem....Pages 172-178 On reducibility in the four color problem....Pages 179-184 Kempe Chains and the Four Colour Problem....Pages 185-225 Front Matter....Pages 227-227 Analytic Extensions of Differentiable Functions Defined in Closed Sets....Pages 228-254 Derivatives, Difference Quotients, and Taylor’s Formula....Pages 256-260 Differentiable Functions Defined in Closed Sets. I....Pages 261-279 Derivatives, Difference Quotients and Taylor’s Formula II....Pages 280-285 Functions Differentiable on the Boundaries of Regions....Pages 286-289 A Function Not Constant on a Connected Set of Critical Points....Pages 290-293 Differentiable Functions Defined in Arbitrary Subsets Of Euclidean Space....Pages 294-302 Front Matter....Pages 227-227 Differentiability of the Remainder Term in Taylor’s Formula....Pages 303-308 Differentiable Even Functions....Pages 309-310 The General Type of Singularity of a Set of 2 n − 1 Smooth Functions of n Variables....Pages 311-322 On the Extension of Differentiable Functions....Pages 323-328 On Ideals Of Differentiable Functions....Pages 329-352 On Totally Differentiable and Smooth Functions....Pages 353-369 On Singularities of Mappings of Euclidean Spaces. I. Mappings of the Plane Into the Plane....Pages 370-406 On functions with bounded n th differences....Pages 407-435 Singularities of Mappings of Euclidean Spaces....Pages 436-452 On Bounded Functions with Bounded n th Differences....Pages 453-454 Front Matter....Pages 455-455 Elementary Structure of Real Algebraic Varieties....Pages 456-467 Quelques propriétés fondamentales des ensembles analytiques-réels....Pages 468-496 Local Properties of Analytic Varieties....Pages 497-536 Tangents to an Analytic Variety....Pages 537-590 Back Matter....Pages 591-592