Limits and the Continuity of Functions

Steven G. Krantz
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Steven G. Krantz: Washington University, Department of Mathematics

Chapter Chapter 5 in A Handbook of Real Variables, 2004, pp 53-69 from Springer

Abstract: Abstract Definition 5.1 Let E ℝ be a set and let f be a real-valued function with domain E. Fix a point P∈ ℝ that is either in E or is an accumulation point of E. We say that f has limit l at P, and we write $$ \mathop {\lim }\limits_{E \mathrel\backepsilon x \to P} f(x) = \ell ,$$ with l a real number, if for each ∈ > 0 there is a δ > 0 such that when x ∈ E and 0

Date: 2004
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DOI: 10.1007/978-0-8176-8128-9_5

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