Does anyone know how to prove the existence of a smooth curve $c$ from the unit interval of the real numbers to a connected smooth manifold $M$ such that $c(0)=p$ and $c(1)=q$ with $p$ and $q$ points on $M$ ? This is a question from Spivak´s Differential Geometry Vol 1. Thanks for the help.
closed as off-topic by José Carlos Santos, A. Goodier, Lazy Lee, Dap, agtortorella Mar 29 '18 at 21:07
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I don't have enough reputation to comment, so I just put it as an answer:
Your question is answered e.g. here: Link