EDB — 0VC

Exercises

1. [0VC] Difficulty:**.Let $(X_i,d_i)$ be compact metric spaces, for $i\in \mathbb{N}$, and choose $y_{i,k}\in X_i$ for $i,k\in \mathbb{N}$. Show that there exists a subsequence $k_h$ such that, for every fixed $i$, $y_{i,k_h}$ converges, that is, the limit $\underset{h\to \infty }{lim}{y}_{i,k_h}$ exists.