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Open subsets of ℕ* are:

Open (i.e., all) subsets of ℕ

*S*^{c}∪ {∞} 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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