A Problem Book in Real Analysis pp 77-96 | Cite as

# Continuity

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## Abstract

• Let *f* : *D* → ℝ and let *c* ∈ *D*. 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 *x* ∈ *D*. If *f* is continuous at each point of a subset *K* ⊆ *D*, 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