topology on three point set?

Let X = {a,b,c}
Construct a topology on X so that there is a compact set that is not closed.

Quote:

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Originally Posted by iamthemanyes

Let X = {a,b,c}
Construct a topology on X so that there is a compact set that is not closed.

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Just make any topology where there is a non-closed set and that non-closed set will be compact since the set if sfinite.

Would this be an example:
{Zero set, X, {a}, {b,c}, {c}, {a,c}}

Then {c} is compact, but NOT closed?

Quote:

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Originally Posted by iamthemanyes

Would this be an example:
{Zero set, X, {a}, {b,c}, {c}, {a,c}}

Then {c} is compact, but NOT closed?

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Right.