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Jaggis
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Would anyone have ideas on how to solve the following problem?
Let (X, τ) be a Hausdorff space and τ0 = {X\K: so that K is compact in (X, τ)}
Show that:
1) τ0 is a topology of X.
2) τ0 is rougher than τ (i.e. τ0 is a genuine subset of τ).
3) (X, τ0) is compact.
This was a question in a recent exam that I took (I failed). I was especially clueless with 3).
Thanks for any help.
Let (X, τ) be a Hausdorff space and τ0 = {X\K: so that K is compact in (X, τ)}
Show that:
1) τ0 is a topology of X.
2) τ0 is rougher than τ (i.e. τ0 is a genuine subset of τ).
3) (X, τ0) is compact.
This was a question in a recent exam that I took (I failed). I was especially clueless with 3).
Thanks for any help.