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Open subsets of ℕ* are:
Open (i.e., all) subsets of ℕ
Sc ∪ {∞} where S is a compact (i.e., finite) subset of _ℕ_
C ∪ {∞} where C is a cofinite subset of _ℕ_
This new space is not discrete
{ ∞ } is not open
It is still Hausdorff
{ x | x ≠ ∞ } is open
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