Definition:Deleted Radius Topology

From ProofWiki
Jump to navigation Jump to search

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 radii to the right of the centers excluded.

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


$\tau$ is referred to as the deleted radius topology.


Also see

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


Sources