Definition:Deleted Diameter Topology

Definition

Let $\struct {\R^2, \tau_d}$ be the real number plane with the usual (Euclidean) topology induced by the Euclidean metric $d$.

Let $\BB$ be the sub-basis of $\tau_d$ defined as the set of all open balls of $\struct {\R^2, d}$ with the horizontal diameters apart from the centers excluded.

Let $\sigma$ be the topology generated from $\BB$.

$\sigma$ is referred to as the deleted diameter topology.

Also see

• Deleted Diameter Topology is Topology

• Definition:Deleted Radius Topology

• Results about the deleted diameter topology can be found here.

Sources

• 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (next): Part $\text {II}$: Counterexamples: $76$. Deleted Diameter Topology