\begin{definition}[Definition:Hjalmar Ekdal Topology]
Let $\tau$ be the topology defined on the (strictly) positive integers $\Z_{>0}$ as follows:
A subset $H$ of $\Z_{>0}$ is in $\tau$ {{iff}} $H$ contains the (immediate) successor of every odd integer that is also in $H$:
:$\tau := \set {H \subseteq \Z_{>0}: 2 n - 1 \in H \implies 2 n \in H}$
Then $\tau$ is referred to as the '''Hjalmar Ekdal topology'''.
The topological space $T = \struct {\Z_{>0}, \tau}$ is referred to as the '''Hjalmar Ekdal space'''.
\end{definition}