Hi,(adsbygoogle = window.adsbygoogle || []).push({});

In Baby Rudin, Thm 3.6 states that If p(n) is a sequence in a compact metric space X, then some subsequence of p(n) converges to a point in X.

Why is it not the case that every subsequence of p(n) converges to a point in X? I would think a compact set would contain every sequence (finite or infinite) that originates within it.

Thanks,

pob

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Convergent sequence in compact metric space

**Physics Forums | Science Articles, Homework Help, Discussion**