Definition:Fort Space

Definition
Let $S$ be an infinite set.

Let $p \in S$ be a particular point of $S$.

Let $\tau_p \subseteq \mathcal P \left({S}\right)$ be a subset of the power set of $S$ defined as:
 * $\tau_p = \left\{{U \subseteq S: p \in \complement_S \left({U}\right)}\right\} \cup \left\{{U \subseteq S: \complement_S \left({U}\right)}\right.$ is finite$\left.{}\right\}$

That is, $\tau_p$ is the set of all subsets of $S$ whose complement in $S$ either contains $p$ or is finite.

Then $\tau_p$ is a Fort topology on $S$, and the topological space $T = \left({S, \tau_p}\right)$ is a Fort space.

Countable Fort Space
If $S$ is countably infinite, $\tau_p$ is a countable Fort topology, and $\left({S, \tau_p}\right)$ is a countable Fort space.

Uncountable Fort Space
If $S$ is uncountable, $\tau_p$ is an uncountable Fort topology, and $\left({S, \tau_p}\right)$ is an uncountable Fort space.

Also see

 * Fort Topology is Topology