width w(X)

For any compact metric space X, the width w(X) of X is the l.u.b. of the set of all real numbers a which satisfy the following condition: for each $\varepsilon > 0$, there exists a finite open cover C of X such that $meshC) < \varepsilon$ and for each chain C' which is a subcollection of C there is a member A of C such that $d(A,{C'}^*) \geq a$.