# Limit Points in Fort Space

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## Theorem

Let $T = \left({S, \tau_p}\right)$ be a Fort space.

Let $x \in S$ such that $x \ne p$.

Then $p$ is the only limit point of $x$.

## Proof

Suppose $y \in S, y \ne p$.

We have by definition of Fort space that $\left\{{y}\right\}$ is open in $T$.

So there is no $z \in \left\{{y}\right\}: z \ne y, z \in U$.

Hence $y$ can not be a limit point of $U$.

## Sources

- 1970: Lynn Arthur Steen and J. Arthur Seebach, Jr.:
*Counterexamples in Topology*... (previous) ... (next): $\text{II}: \ 23 - 24: \ 7$