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.
The majority of my readers will be greatly disappointed to learn that by this commonplace observation the secret of continuity is to be revealed.
Julius Wilhelm Richard Dedekind (1831–1916)
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© 2010 Springer Science+Business Media, LLC
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Aksoy, A.G., Khamsi, M.A. (2010). Continuity. In: A Problem Book in Real Analysis. Problem Books in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-1296-1_5
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DOI: https://doi.org/10.1007/978-1-4419-1296-1_5
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