Curves and Surfaces > Curves > Special Curves > Topology
Curves with special topological properties.
Orientation Closed curves are often given an orientation.
Compactness A bounded closed curve is said to be compact.
Completeness  
Convex Curves Curves whose tangent lines intersect them only once.
Covering Curves  

Orientation

A closed curve can be given an orientation; if one walks around the border in such a way as to keep the interior of the region on one's left at all times, the border is said to be positively oriented. If the boundary is traversed in the opposite direction, then it is said to be negatively oriented. An ellipse could be given an orientation, for example; if it were traversed counterclockwise, it would have a positive orientation.

Compactness

A curve that is both closed and bounded is said to be compact; one example of such a curve is a circle.

Completeness

 

Convex Curves

A curve is convex if it lies entirely on one side of its tangent line at all points on the curve. An example of such a curve is the circle.

Covering Curves