Hassler Whitney Collected Papers Volume I

1. Front Matter

   Pages i-xiv

   PDF

2. Introduction

   1. Moscow 1935: Topology Moving Toward America

      • Hassler Whitney

      Pages 1-21

3. Graphs and Combinatorics

   1. Front Matter

      Pages 23-23

      PDF

   2. A Theorem on Graphs

      • Hassler Whitney

      Pages 24-36

   3. Non-Separable and Planar Graphs

      • Hassler Whitney

      Pages 37-59

   4. Congruent Graphs and the Connectivity of Graphs

      • Hassler Whitney

      Pages 61-79

   5. The Coloring Of Graphs

      • Hassler Whitney

      Pages 80-110

   6. A Set of Topological Invariants for Graphs

      • Hassler Whitney

      Pages 111-115

   7. On the Classification of Graphs

      • Hassler Whitney

      Pages 116-124

   8. 2-Isomorphic Graphs

      • Hassler Whitney

      Pages 125-134

   9. Planar Graphs

      • Hassler Whitney

      Pages 135-146

   10. On the Abstract Properties of Linear Dependence

       • Hassler Whitney

       Pages 147-171

   11. A numerical equivalent of the four color map Problem

       • Hassler Whitney

       Pages 172-178

   12. On reducibility in the four color problem

       • Hassler Whitney

       Pages 179-184

   13. Kempe Chains and the Four Colour Problem

       • Hassler Whitney, W. T. Tutte

       Pages 185-225

4. Differentiable Functions and Singularities

   1. Front Matter

      Pages 227-227

      PDF

   2. Analytic Extensions of Differentiable Functions Defined in Closed Sets

      • Hassler Whitney

      Pages 228-254

   3. Derivatives, Difference Quotients, and Taylor’s Formula

      • Hassler Whitney

      Pages 256-260

   4. Differentiable Functions Defined in Closed Sets. I

      • Hassler Whitney

      Pages 261-279

   5. Derivatives, Difference Quotients and Taylor’s Formula II

      • Hassler Whitney

      Pages 280-285

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 We also include the introduction to his book Geometric Integration Theory, and one previously unpublished manuscript on the four-color problem.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.

• Manuscript
• children
• classification
• education
• educational system
• information
• mathematics
• system
• time
• topological invariant
• topology
• university

• Department of Mathematics, University of Warwick, Coventry, England

  James Eells

• Department of Mathematics, University of Utah, Salt Lake City, USA

  Domingo Toledo

Policies and ethics