Completely regular not implies normal

Statement
A completely regular space need not be a normal space.

Example of the Moore plane
The Moore plane or Niemitzky plane or tangent disk topology is defined as follows: as a set, it is the upper half-plane, along with the bounding real line. The topology is described by the following basis:


 * All open disks that lie completely inside the upper half-plane
 * For points which are on the bounding line, the union of such a point with an open disk tangent to the bounding line at that point

We have that:


 * Moore plane is completely regular
 * Moore plane is not normal