PROPERTIES OF COMPACT SETS
Compact Set : A subset K of a metric space X is called compact if every open cover has a finite sub cover. The compact sets has come properties . Here we see their properties with proofs. Property 1. Closed Subsets Of Compact Sets are Compact . proof : Property 2 : The intersection of any collection of compact subsets of a metric space with finite intersection property is non-empty. Proof : Property 3: Compact subsets of metric spaces are bounded. Proof : property 4 : Compact subsets of metric spaces are closed. Proof : People also see : 1. What is an open cover? 2. What is cantor intersection theorem ? 3. What is a metric space? 4. What is a closed set? 5. What is a Pseudo-metric ?