What are some small examples of what it means to be $C^0$-small?
The context I'm working in has this example: Let $u:\mathbb{R}\to X$ be a smooth curve where $X$ is a smooth manifold. Then given the tangent bundle $TX\to X$, we have the pullback bundle $u^{*}TX \to \mathbb{R}$. Now consider the space of sections $\Gamma(\mathbb{R}, u^{*}TX)$ and take $\psi: \mathbb{R}\to u^{*}TX$ to be one of these sections. They call $\psi$ "$C^{0}$-small"—what does that mean? If I'm not mistaken, $\psi$ should be viewed as a flowline... at least the exponential map of $\psi$ can perturb a flowline.
Thanks in advance!