Definition:Double Pointed Real Number Line

Theorem
Let $T_\R = \struct {\R, \tau_d}$ be the real number space under the usual (Euclidean) topology.

Let $T_D = \struct {D, \tau_D}$ be the indiscrete topology on the doubleton $D = \set {a, b}$.

Let $T = T_\R \times T_D$ be theproduct space of $T_\R$ and $T_D$.

$T$ is known as the double pointed real number space.