# Category:Fort Spaces

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This category contains results about Fort Spaces.

Definitions specific to this category can be found in Definitions/Fort Spaces.

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**.

## Pages in category "Fort Spaces"

The following 25 pages are in this category, out of 25 total.

### C

### F

- Fort Space is Compact
- Fort Space is Completely Normal
- Fort Space is Excluded Point Space with Finite Complement Space
- Fort Space is not Extremally Disconnected
- Fort Space is Regular
- Fort Space is Scattered
- Fort Space is Sequentially Compact
- Fort Space is T0
- Fort Space is T1
- Fort Space is T5
- Fort Space is Totally Separated
- Fort Space is Zero Dimensional
- Fort Topology is Topology