> [!definition] > > Let $E, F$ be [[Banach Space|Banach spaces]] and $U \in \cn(0)^o$ be an [[Open Set|open]] [[Neighbourhood|neighbourhood]] of $0$, then a [[Function|function]] $u: U \to F$ is *little-o* of $x$ if > $ > \lim_{x \to 0} \frac{\norm{u(x)}_F}{\norm{x}_E} = 0 > $ > [!definition] > > Let $E, F$ be [[Topological Vector Space|topological vector spaces]] and $U \in \cn(0)^o$ be an open neighbourhood of $0$. A mapping $\psi: U \to F$ is **tangent to** $0$, if given any neighbourhood $W \in \cn(0)$ in $F$, there exists a neighbourhood $V \in \cn(0)$ and a function $o(t)$ such that > $ > \psi(tV) \subset o(t) W > $