# Definition:Region/Plane

 It has been suggested that this page or section be merged into Definition:Open Region.  Reason: This is defined in T&P just as "region" but it is clear from criterion $(1)$ that the region under discussion is definitely open. (Discuss)
A point set $R$ in the plane is a region if and only if:
$(1): \quad$ Each point of $R$ is the center of a circle all of whose elements consist of points of $R$
$(2): \quad$ Each point of $R$ can be joined by a curve consisting entirely of points of $R$.