I am a little confused about some terminology when we talk about curves and regions (in the context of vectors for example). Are these correct? Curve Terminology: Smooth: A curve C is said to be smooth if it is infinitely differentiable everywhere in its domain. Continuous: A curve C is said to be continuous if it is once differentiable everywhere in its domain. Simple: A curve C is said to be simple if it does not cross itself. Region Terminology: Connected: A region D in R^3 is said to be connected if any two points in D can be joined by a smooth curve completely in D. Simply Connected: A region D in R^3, is said to be be simply connected if any simple closed curve inside D can be shrunk down to a point inside D.