I am a little confused about some terminology when we talk about curves and regions (in the context of vectors for example).(adsbygoogle = window.adsbygoogle || []).push({});

Are these correct?

Curve Terminology:

Smooth:A curve C is said to besmoothif it is infinitely differentiable everywhere in its domain.

Continuous:A curve C is said to becontinuousif it is once differentiable everywhere in its domain.

Simple:A curve C is said to besimpleif it does not cross itself.

Region Terminology:

Connected:A region D in R^3 is said to beconnectedif 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 besimply connectedif any simple closed curve inside D can be shrunk down to a point inside D.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Curve Terminology

**Physics Forums | Science Articles, Homework Help, Discussion**