Definition:Double Pointed Real Number Line

Theorem

Let $T_\R = \struct {\R, \tau_d}$ be the real number line with 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 the product space of $T_\R$ and $T_D$.

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

Also see

• Results about the double pointed real number line can be found here.

Sources

• 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.): Part $\text {II}$: Counterexamples: $62$. Double Pointed Reals