Definition talk:Smooth Curve

Is a non-compact connected manifold of dimension 1 by definition identical with the Real Number Line? If so, we need a page to demonstrate this -- and then it may not be necessary to define the domain as being such a manifold, we can just make it the Real Number Line. If they are not necessarily the same object, then we may need to reword this definition. --prime mover (talk) 12:05, 16 September 2014 (UTC)