In this paper we define the notions of weighted covering number and weighted separation number for convex sets, and compare them to the classical covering and separation numbers. This sheds new light on the equivalence of classical covering and separation. We also provide a formula for computing these numbers via a limit of classical covering numbers in higher dimensions.
Bibliographical noteFunding Information:
✩ Both authors were partially supported by ISF grant 865/07. This work is part of the M.Sc. thesis of the second named author. * Corresponding author. E-mail address: email@example.com (S. Artstein-Avidan).
- Convex sets
- Covering numbers
- Separation numbers
- Weighted covering