Definition:Continuous Real Function/Everywhere
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Definition
Let $f: \R \to \R$ be a real function.
Then $f$ is everywhere continuous if and only if $f$ is continuous at every point in $\R$.
Also known as
Some sources take the everywhere nature of such a real function as understood, and merely refer to it as a continuous (real) function.
Sources
- 1959: E.M. Patterson: Topology (2nd ed.) ... (previous) ... (next): Chapter $\text {II}$: Topological Spaces: $\S 11$. Continuity on the Euclidean line
- 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $\S 1.4$: Continuity: Definition $1.4.4$
