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

Orientation

A closed surface can be given an orientation; if one moves around the boundary in such a way as to keep the interior of the region underneath one at all times, the boundary is said to be orientable. A sphere could be given an orientation, for example, but a klein bottle could not.

Compactness

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

Completeness

 

Convex Surfaces

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

Covering Curves