Definition:Continuous Extension/Real Function
< Definition:Continuous Extension(Redirected from Definition:Real Continuous Extension)
Jump to navigation
Jump to search
Definition
Let $A$, $B \subseteq \R$ be subsets of the real numbers such that $A \subseteq B$.
Let $f: A \to \R$ and $g: B \to \R$ be continuous real functions.
Then $g$ is a continuous extension of $f$ if and only if:
- $\forall x \in A : \map f x = \map g x$