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Topology of ℝ and Continuity

  • Houshang H. Sohrab

Abstract

Most interesting sets in mathematics have structures (algebraic, geometric, topological, … ). For example, the set ℝ of real numbers is, algebraically, a field; i.e., it satisfies the nine axioms A1A4, M4M4 and D listed at the beginning of Chapter 2. Given this field structure, the most (algebraically) desirable functions ø : ℝ → ℝ are those that are faithful to the field properties; i.e., preserve them. Such maps are called the morphisms of the field ℝ.

Keywords

Limit Point Lipschitz Function Open Interval Open Cover Lipschitz Constant 
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 Science+Business Media New York 2003

Authors and Affiliations

  • Houshang H. Sohrab
    • 1
  1. 1.Mathematics DepartmentTowson UniversityTowson

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