Abstract Manifolds

  • Anatolij T. Fomenko
  • Tosiyasu L. Kinii


In Chapter 3 we defined manifolds in ℝ n (see Definition 3.3.1), and we remarked that a more abstract definition is possible, so that a manifold does not have to exist in any ℝ n . We introduce this definition in this chapter, and also a technical tool useful in the study of manifolds, called partitions of unity. The chapter closes with an application to the generation of topographic maps.


Smooth Manifold Open Disk Mountain Pass View Direction Coordinate Chart 
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Copyright information

© Springer Japan 1997

Authors and Affiliations

  • Anatolij T. Fomenko
    • 1
  • Tosiyasu L. Kinii
    • 2
    • 3
  1. 1.Department of Differential Geometry and Application, Faculty of Mathematics and MechanicsMoscow State UniversityMoscowRussia
  2. 2.Laboratory of Digital Art and TechnologyTokyo, 113Japan
  3. 3.Senior Partner of MONOLITH Co. Ltd.Tokyo, 106Japan

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