# if arbitrary intersection of compact sets is empty, then there exists at least two sets that are disjoint?

if arbitrary intersection of compact set is empty, then there exists at least two sets that are disjoint?

Generally, I know the argument is false as nested intersection of open sets are empty, but there is not pair-wise disjoint. How about compact sets (closed and bounded in real line?)

• Cover a circle with three arcs … – Daniel Fischer Oct 19 '16 at 21:14
• Let $A = [2,5]$, $B = [4,7]$ and $C = [0,3]\cup[6,9]$. – Joey Zou Oct 19 '16 at 21:15
• Use pairs.   – Did Oct 26 '16 at 8:12