Definition:Hjalmar Ekdal Topology

Definition
Let $\tau$ be the topology defined on the (strictly) positive integers $\Z_{>0}$ as follows:

A subset $H$ of $\Z_{>0}$ is in $\tau$ $H$ 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.

Also see

 * Hjalmar Ekdal Topology is Topology