Difference between revisions of "Sequentially compact"
Jump to navigation
Jump to search
| Line 1: | Line 1: | ||
| − | A [[topological space]] X is called '''sequentially compact''' if every [[sequence]] in X has a convergent subsequence. A [[metric space]] | + | A [[topological space]] X is called '''sequentially compact''' if every [[sequence]] in X has a convergent subsequence. A [[metric space]] is sequentially compact if and only if it's [[compact]]. |
[[Category: Mathematics]] | [[Category: Mathematics]] | ||
Revision as of 04:11, March 31, 2007
A topological space X is called sequentially compact if every sequence in X has a convergent subsequence. A metric space is sequentially compact if and only if it's compact.