If P is a topological property, then a space (X, τ) is said to be minimal P (respectively, maximal) if (X,τ) has property P but no topology on X which is strictly smaller (respectively, strictly larger ) than τ has P.
A topological space is called KC space if every compact subset is closed.
A topological space is called strongly KC space if every countably compact subset is closed.
I know (strongly) KC – space is topological property.
I want to know:
Is there a example of a minimal KC but not minimal strongly KC – space?
It is a fact that an infinite minimal strongly KC space has a trivial convergent sequence, but it does not hold for minimal KC space. I want an easy example to show it.