Ordinary topology on infinite subsets
= Ordinary topology on infinite subsets
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The ordinary topology on $[\mathbb N]^\omega$ has basic sets $[s]=\{X:s\sqsubset X\}$ for finite $s$. It is the <product topology> on increasing enumerations, and also the subspace topology on infinite-subset <indicator functions> in $\{0,1\}^{\mathbb N}$.