- #1
pob1212
- 21
- 0
Hi,
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
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