EDB — 0VP

[0VP] Topics:compact.Prerequisites:[0V6]↺↻.

Let $(X,d)$ be a metric space, and let $A_n\subseteq X$ be compact non-empty subsets such that $A_{n+1}\subseteq A_n$: then ${\bigcap }_{n\in \mathbb{N}}{A}_n\ne \varnothing$.

(This result can be derived from [0J6]↺↻; but try to give a direct demonstration, using the characterization of ”compact” as ”sequentially compact ”, i.e. the first point in [0V3]↺↻).