Ellentuck topology
= Ellentuck topology
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{title2=$\tau^*$}
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For a finite set $s$ and an infinite set $A$ lying above $\max s$, put
$$
[s,A]=\{s\cup B:B\in[A]^\omega\}.
$$
These sets form the basic neighborhoods of the Ellentuck topology, also called the star topology. It is finer than the <ordinary topology on infinite subsets>. Every basic neighborhood is a <clopen set> in the Ellentuck topology, and a <closed set> in the ordinary topology.