I have a theorem here which says
If $M \in \mathbb{R}^n$ is compact, connected and locally connected and $a,b \in M$ then there is for all $\epsilon>0$ a $\delta>0$ where $\delta \leq \epsilon$ such that whenever $$||a-b|| < \delta$$ there is a continuous path from a to b that lies in $N_\epsilon(a) \cap M$ as well as in $N_\epsilon(b) \cap M$.
In terms of the notation: $N_{\delta} (a)=\{x \in \mathbb{R}^n| ||x-a| < \delta\}$ is the $\delta$ neighbourhood of $a \in \mathbb{R}^n$
What is this theorem trying to say?
What does $N_\epsilon(a) \cap M$ mean?