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.
KeywordsLimit Point Lipschitz Function Open Interval Open Cover Lipschitz Constant
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