Definition:Nested Interval Topology

Definition
Let $S = \openint 0 1$ denote the open real interval:
 * $\openint 0 1 = \set {x \in \R: 0 < x < 1}$

Let $\tau$ be the topology defined on $\openint 0 1$ by defining the open sets $U_n$ as:


 * $\forall n \in \N_{>0}: U_n := \openint 0 {1 - \dfrac 1 n}$

together with $\O$ and $S$ itself.

Then $\tau$ is referred to as the nested interval topology.

The topological space $T = \struct {S, \tau}$ is referred to as the nested interval space.

Also see

 * Nested Interval Topology is Topology