M monster Dec 2008 73 0 May 23, 2010 #1 A am revising for my exam and have come across a proof i'm struggling with as i struggle with prooofs involving compactness, If E is a subset of \(\displaystyle R^n\) Show that E is compact if and only if E is closed and bounded. I know this to be true but don't know how to prove it. Any help here would be greatly appreciated, Cheers

A am revising for my exam and have come across a proof i'm struggling with as i struggle with prooofs involving compactness, If E is a subset of \(\displaystyle R^n\) Show that E is compact if and only if E is closed and bounded. I know this to be true but don't know how to prove it. Any help here would be greatly appreciated, Cheers

T tonio Oct 2009 4,261 1,836 May 24, 2010 #2 monster said: A am revising for my exam and have come across a proof i'm struggling with as i struggle with prooofs involving compactness, If E is a subset of \(\displaystyle R^n\) Show that E is compact if and only if E is closed and bounded. I know this to be true but don't know how to prove it. Any help here would be greatly appreciated, Cheers Click to expand... Too long to do it here, but it's completely standard. Google "Heine-Borel Theorem" Tonio Reactions: monster

monster said: A am revising for my exam and have come across a proof i'm struggling with as i struggle with prooofs involving compactness, If E is a subset of \(\displaystyle R^n\) Show that E is compact if and only if E is closed and bounded. I know this to be true but don't know how to prove it. Any help here would be greatly appreciated, Cheers Click to expand... Too long to do it here, but it's completely standard. Google "Heine-Borel Theorem" Tonio