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Transversality

  • Morris W. Hirsch
Part of the Graduate Texts in Mathematics book series (GTM, volume 33)

Abstract

Consider the following statements :
  1. 1.

    If f :S2 → ℝ2 is C1 then f-1 (y) is finite for “most“ points y ∈ ℝ.

     
  2. 2.

    Two lines in ℝ3 do not intersect “in general.“

     
  3. 3.

    If f: ℝ→ ℝ is C1, “almost all“ horizontal lines in ℝ × ℝ are nowhere tangent to the graph of f.

     
  4. 4.

    “Generically“ a C1 immersion S1 → ℝ2 has only a finite number of crossing points.

     

Keywords

Measure Zero Strong Topology Differential Topology Submanifold Complex Residual Subset 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1976

Authors and Affiliations

  • Morris W. Hirsch
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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