  Following Frink's characterization of completely regular spaces, we say that
a regular T_1-space is an RC-space whenever the family of all regular open sets
constitutes a regular normal base. Normal spaces are RC-spaces and there exist
completely regular spaces which are not RC-spaces. So the question arises,
which of the known examples of completely regular and not normal spaces are
RC-spaces. We show that the Niemytzki plane and the Sorgenfrey plane are
RC-spaces.
