Solution
= Solution
\b[Not a <topology>.] Each singleton $\{n\}$ with $n>0$ is finite and hence belongs to the proposed family, but their union $\{1,2,3,\ldots\}$ is infinite and excludes zero, so does not belong. The arbitrary-union axiom fails.
= Solution
\b[Not a <topology>.] Each singleton $\{n\}$ with $n>0$ is finite and hence belongs to the proposed family, but their union $\{1,2,3,\ldots\}$ is infinite and excludes zero, so does not belong. The arbitrary-union axiom fails.