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Continuity

  • Asuman G. Aksoy
  • Mohamed A. Khamsi
Chapter
Part of the Problem Books in Mathematics book series (PBM)

Abstract

• Let f : D → ℝ and let cD. We say that f is continuous at c if for every ε > 0 there exists a δ > 0 such that \(\left| {f\left( x \right) - f\left( c \right)} \right|\, < \,\varepsilon \) whenever \(\left| {x - c} \right|\, < \,\delta \) and xD. If f is continuous at each point of a subset KD, then f is said to be continuous on K. Moreover, if f is continuous on its domain D, then we simply say that f is continuous.

Keywords

Bounded Interval Lipschitz Function Cauchy Sequence Continuity Solution Continuity Problem 
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, LLC 2010

Authors and Affiliations

  1. 1.Department of MathematicsClaremont McKenna CollegeClaremontUSA
  2. 2.Department of Mathematical SciencesUniversity of Texas at El PasoEl PasoUSA

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