Consider a connected manifold $M$ and two distinct points $p,q$ on the manifold. Is it true that there exists a chart containing both? How can one prove this result?
OBS: I've seen an answer on the internet which relied on taking a path from $p$ to $q$, using a tubular neighbourhood and arguing that two charts on $p$ and $q$ together with the neighbourhood would give something diffeomorphic to $\mathbb{R}^n$, but this isn't clear to me at all.