Difference between revisions of "Compact space"
Jump to navigation
Jump to search
(New page: A topological space '''X''' is said to be compact, if every open cover of '''X''' contains a finite subcover. Category:Mathematics) |
|||
| (9 intermediate revisions by 6 users not shown) | |||
| Line 1: | Line 1: | ||
A [[topological space]] '''X''' is said to be compact, if every [[open cover]] of '''X''' contains a finite subcover. | A [[topological space]] '''X''' is said to be compact, if every [[open cover]] of '''X''' contains a finite subcover. | ||
| − | [[Category: | + | '''Important Theorem''': A [[metric space]] is compact if and only if it's [[complete (mathematics)|complete]] and [[totally bounded space|totally bounded]]. |
| + | [[Category:Topology]] | ||
Latest revision as of 00:57, May 16, 2012
A topological space X is said to be compact, if every open cover of X contains a finite subcover.
Important Theorem: A metric space is compact if and only if it's complete and totally bounded.