Region

Boundary

The subset of a region not belonging to the inerior of the region.

Closed

The region contains all of its boundary points.

Open

The region contains none of its boundary points.

Simply-Connected

One piece with no holes.

Bounded

The region has finite size.

Simple

2D

Vertically Simple

(Type 1 Region) A region bounded by the vertical lines and , and the curves and , where and

Horizonally Simple

(Type 2 Region) A region bounded by the horizontal lines and , and the curves and , where and

3D

X-Simple

If the 2D region is the projection of 3D region onto the -plane and is exclusively bounded above and below by surfaces and then

and then is an -simple region.

Y-Simple

If the 2D region is the projection of 3D region onto the -plane and is exclusively bounded above and below by surfaces and then

and then is a -simple region.

Z-Simple

If the 2D region is the projection of 3D region onto the -plane and is exclusively bounded above and below by surfaces and then

and then is a -simple region.