Definition:Concentric Circle Topology
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Definition
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.
Also see
- Results about the concentric circle topology can be found here.
Sources
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.): Part $\text {II}$: Counterexamples: $97$. Concentric Circles