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clean up deprecated proof of topology
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StevenClontz authored Oct 8, 2024
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Expand Up @@ -15,19 +15,3 @@ and {S194}.

Defined as counterexample #52 ("Nested Interval Topology")
in {{doi:10.1007/978-1-4612-6290-9}}.

<!-- [[Proof of Topology]]
1. Note that $X \in N$ by definition and $U_1=(0,1-\frac{1}{1})=(0,0)= \emptyset$ thus $\emptyset \in N$.
2. Let $I$ be any indexing set of $n \in \mathbb{N}$ where $\bigcup\limits_{n \in I} U_n$ where $U_n \in N$. Thus
\begin{align*}
\bigcup\limits_{n \in I} U_n &= U_{max(n) \in I}, or X
\end{align*}
Which are both open.
3. Let $I$ be any finite indexing set of $n \in \mathbb{N}$. Thus
\begin{align*}
\bigcap\limits_{n \in I} U_n &= U_{min(I)}
\end{align*}
which is an open set so any finite union of open sets is open.
-->

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