- #1
qinglong.1397
- 108
- 1
Homework Statement
Prove that a subset [tex]A[/tex] of [tex]R^{n}[/tex] is compact if and only if every nested sequence [tex]\{A_n\}_{n=1}^{\infty}[/tex] of relatively closed , non-empty subsets of [tex]A[/tex] has non-empty intersection
The Attempt at a Solution
I can prove [tex]\rightarrow[/tex], but not [tex]\leftarrow[/tex]. Would you please give me a hint? Thank you very much!