# Category:Modified Fort Space

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This category contains results about Modified Fort Space.

Let $N$ be an infinite set.

Let $\set a$ and $\set b$ be singleton sets such that $a \ne b$ and $a, b \notin N$.

Let $S = N \cup \set a \cup \set b$.

Let $\tau_{a, b}$ be the set of subsets of $S$ defined as:

- $\tau_{a, b} = \set {H \subseteq N} \cup \set {H \subseteq S: \paren {a \in H \lor b \in H} \land N \setminus H \text { is finite} }$

That is, a subset $H$ of $S$ is in $\tau_{a, b}$ if and only if either:

- $(1): \quad H$ is any subset of $N$

or:

- $(2): \quad$ if $a$ or $b$ or both are in $H$, then $H$ is in $S$ only if it is cofinite in $S$, that is, that it contains all but a finite number of points of $S$ (or $N$, equivalently).

Then $\tau_{a, b}$ is a **modified Fort topology** on $a$ and $b$, and the topological space $T = \struct {S, \tau_{a, b} }$ is a **modified Fort space**.

## Pages in category "Modified Fort Space"

The following 15 pages are in this category, out of 15 total.

### M

- Modified Fort Space is Compact
- Modified Fort Space is not Locally Connected
- Modified Fort Space is not T2
- Modified Fort Space is not T3, T4 or T5
- Modified Fort Space is not Totally Separated
- Modified Fort Space is not Zero Dimensional
- Modified Fort Space is Scattered
- Modified Fort Space is Sequentially Compact
- Modified Fort Space is T1
- Modified Fort Space is Totally Disconnected
- Modified Fort Topology is Topology