Definition:Altered Long Line/Greatest Element

Definition

Let $T = \struct {S, \tau_p}$ denote the altered long line on the long line $L$.

Let $p$ be the point which is not an element of $L$ upon which the topology $\tau_p$ is generated.

$p$ is the greatest element of $S = L \cup \set p$.

Sources

• 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous): Part $\text {II}$: Counterexamples: $47$. An Altered Long Line