EDB — 0VB

Exercises

1. [0VB] Let \(n≥ 1\) be natural. Let \((X_ i,d_ i)\) be compact metric spaces, for \(i=1,\ldots n\); choose \(y_{i,k}∈ X_ i\) for \(i=1,\ldots n\) and \(k∈ℕ\). Show that there exists a subsequence \(k_ h\) such that, for every fixed \(i\), \(y_{i,k_ h}\) converges, that is, the limit \(\lim _{h→∞} y_{i,k_ h}\) exists.