- #1
Swapnil
- 459
- 6
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.
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.