\begin{definition}[Definition:Concentric Circle Topology]
:rightthumb280pxOpen Set of $T$
Let $C_1$ and $C_2$ be concentric circles in the Cartesian plane $\R^2$ such that $C_1$ is inside $C_2$.
Let $S = C_1 \cup C_2$.
Let $\BB$ be the set of sets consisting of:
:all singleton sets of $C_2$
:all open intervals on $C_1$ each together with its projection from the center of the circles onto $C_2$ except for the midpoint.
$\BB$ is then taken to be the sub-basis for a topology $\tau$ on $S$.
Thus $\tau$ is referred to as the '''concentric circle topology'''.
The topological space $T = \struct {S, \tau}$ is referred to as the '''concentric circle space'''.
\end{definition}