I keep seeing the sentence " you can find a reagularly parametrized smooth curve through each point in each direction"
"There are three smooth paths starting there and lying on the boundary of the cube - the edges ( almost any parametrization should work)" //edit : the last sentence came from how to prove boundary of the cube isnt smooth manifold, that was an assumption
and indeed its seems correct, and by taking parametrization as graph, its seems to be correct - but this is just on one direction. what about the others ?
what is a formal explanation for this ?