[Unlocked] Let K1 ⊇ K2
Can someone please help with a Topology Assignment.
Let (X, T ) be a Hausdorff topological space and let K1 ⊇ K2 ⊇ . . . ⊇ Kn ⊇ . . . be an infinite sequence of non-empty compact subsets of X. Show that Kn ̸= ∅. i.e. there exists a point x ∈ X such that x ∈ Kn for all n ≥ 1.
Please see attached image of the question typed up.