= Dense countable family of cofinite infinite subsets
{title2=$D=\{X\subseteq\mathbb N:X\text{ is cofinite}\}$}
In the <ordinary topology on infinite subsets>, the family $D$ of <cofinite sets> is a <countable set>, a <dense> and a <meagre set>. Countability follows by indexing its members by their finite complements. Each singleton is closed with empty interior, while every basic cylinder with finite initial segment $s$ contains $s\cup\{n:n>\max s\}$. Consequently $D$ is not a <nowhere dense set>. This example uses the ordinary cylinder topology, rather than the <Ramsey cone topology>.
Back to article page
