Topology of ℝ and Continuity

Houshang H. Sohrab
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Houshang H. Sohrab: Towson University, Mathematics Department

Chapter 4 in Basic Real Analysis, 2003, pp 113-155 from Springer

Abstract: 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 A1 – A4, M4 – M4 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 (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1007/978-0-8176-8232-3_4

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