User:Anghel/Sandbox

Theorem
Let $S \subseteq \R^m$ be an open subset of the Euclidean space $R^m$.

Let $\gamma: \left[{a \,.\,.\, b}\right] \to S$ be a path in $S$.

Then there exists a normal subdivision $\left\{{x_0, x_1, \ldots, x_{n-1}, x_n}\right\}$ of the closed interval $\left[{a \,.\,.\, b}\right]$ and a radius $r \in \R_{>0}$ such that:


 * For all $\epsilon \in \left({0 \,.\,.\, K}\right)$,


 * $\bigcup_{i \mathop = n} B_r \left({\gamma \left({x_i}\right) }\right)$