\begin{definition}[Definition:Nested Interval Topology]
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'''.
\end{definition}