Let $K$ be a subset of the real line and consider the statements
a) K is compact
b) Every cover of $K$ by intervals of the type $[a,b]$ with $b-a>0$ has a finite subcover.
Does a) imply b)?
Does b) imply a)?
Let $K$ be a subset of the real line and consider the statements
a) K is compact
b) Every cover of $K$ by intervals of the type $[a,b]$ with $b-a>0$ has a finite subcover.
Does a) imply b)?
Does b) imply a)?