= Meagreness of the Ramsey cone topology
The whole <space of infinite subsets of the natural numbers> is a <meagre set> in the <Ramsey cone topology>. For $D_j=\{X:\min X=j\}$, the closure is $\{X:j\in X\}$, which has empty interior: every infinite ground set can be thinned to omit $j$. Thus all $D_j$ are <nowhere dense>, while their countable union is the whole space. In contrast, the whole space is not meagre in either the <Ellentuck topology> or the <ordinary topology on infinite subsets>.
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