Definition:Continuous Real Function/Open Interval
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Definition
Let $f$ be a real function defined on an open interval $\openint a b$.
Then $f$ is continuous on $\openint a b$ if and only if it is continuous at every point of $\openint a b$.
Sources
- 1961: David V. Widder: Advanced Calculus (2nd ed.) ... (previous) ... (next): $1$ Partial Differentiation: $\S 2$. Functions of One Variable: $2.1$ Limits and Continuity
- 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 9.1$
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): continuous function