(1) is completely composed of interior points;

(2) Connectivity, that is, any two points in a point set can be connected by a broken line, and all points on the broken line are in this open domain.

Closed domain: open domain and its boundary.

Region: a point set consisting of open domain, closed domain or open domain and some boundary points.

Extended data:

Let e be a point set on the plane and p be a point on the plane. If point P has a neighborhood, P is called an interior point of E ... If all points of point set E are interior points, then E is called an open set.

Connected open sets are called regions or open sets. For example:

An open area together with its boundary is called a closed area. For example:

For point set E, if there is a positive number k, so that the distance between all points and point A does not exceed k, that is, everything holds, then E is called bounded point set, otherwise it is called unbounded point set.

For example, it is a bounded closed area. This is an unbounded open area.

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