EDB — 0J6

[0J6] Topics:compact sets.Prerequisites:[0J5]↺↻. Note:For the real case, see [0BF]↺↻. For the case of metric spaces, see [0VP]↺↻..

Let \((X,𝜏)\) be a \(T_ 2\) topological space and let \(A_ n⊆ X\) be compact nonempty subsets such that \(A_{n+1}⊆ A_ n\): then \(⋂_{n∈ℕ} A_ n≠ ∅\).

What happens if the space is not \(T_ 2\)?