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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$.
next up previous contents index
Next: List of examples Up: Definitions Previous: widely connected
Janusz J. Charatonik, Pawel Krupski and Pavel Pyrih
2001-11-30