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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]]