# Unstable

Let $(X,d_1)$ and $(Y,d_2)$ be metric spaces. Let $a \in X$ and let $f \colon X \rightarrow Y$. We say that $f$ is unstable at $a$ provided for each $\epsilon > 0$ there exists a mapping $g$ from $X$ into $Y$ such that $d_2(f(x),g(x))<\epsilon$ for $x \in X$ and $f(a)$ in $g(X)$.