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Make explanation of second countability more clear!
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prescientmoon committed Dec 4, 2024
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Expand Up @@ -128,7 +128,7 @@ \section{Topological manifolds}\label{sec:top_manifolds}
\label{fig:1.2-charts}
\end{figure}

Don't get scared by conditions (i) and (ii) in the definition of topological manifolds: they are only needed to make sure that there are not too few open sets (Hausdorff) and not too many (second countable).
Don't get scared by conditions (i) and (ii) in the definition of topological manifolds: they are only needed to make sure that there are not too few open sets (Hausdorff) and that they are are smaller than your mom (second countable).

\begin{example}
With our definition, a countable collections of points with the discrete topology is a $0$-dimensional topological manifold.
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