Local Structure on the Real Line

Mangatiana A. Robdera
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Mangatiana A. Robdera: Al Akhawayn University, School of Science and Engineering

Chapter 8 in A Concise Approach to Mathematical Analysis, 2003, pp 213-240 from Springer

Abstract: Abstract In previous chapters, we considered the algebraic and order structures ℝ of the set of real numbers. We have seen that properties such as convergence of sequences, continuity and differentiability of functions, are all defined locally around some given point. In this chapter, we shall study ℝ further by considering its features locally around each of its points. The generalization of such an approach to a more abstract setting is of great importance in analysis. In this chapter, we will discuss only subsets of the real line.

Date: 2003
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DOI: 10.1007/978-0-85729-347-3_8

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