Difference between revisions of "Compact space"
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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. | ||
| − | Important Theorem: A [[metric space]] is compact if and only if it's [[complete (mathematics)|complete]] and [[totally bounded space|totally bounded]]. | + | '''Important Theorem''': A [[metric space]] is compact if and only if it's [[complete (mathematics)|complete]] and [[totally bounded space|totally bounded]]. |
[[Category:Topology]] | [[Category:Topology]] | ||
Revision as of 22:33, April 10, 2007
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.