Definition:Telophase Topology

Definition

Let $S = \closedint 0 1 \cup \set {1^*}$ where:

$\closedint 0 1$ is the closed unit interval $\set {x \in \R: 0 \le x \le 1}$

$1^*$ is a second right hand endpoint of $\closedint 0 1$.

Let $\BB$ be a local basis defined as:

$\BB = \set {\openint a 1 \cup \set {1^*}: a \in \closedint 0 1}$

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

$\tau$ is referred to as the telophase topology.

Also see

• Telophase Topology is Topology

• Results about the telophase topology can be found here.

Linguistic Note

The word telophase is a term in biology for a late phase in the process of cell division in which the interior components of the daughter cells have completely distinguished themselves and have divided into separate clusters ready for the stage where the cell splits into two.

The significance of the name in the context of the telophase topology remains to be established.

Sources

• 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.): Part $\text {II}$: Counterexamples: $73$. Telophase Topology