- Title
- Compact convex sets with prescribed facial dimensions
- Creator
- Roshchina, Vera; Sang, Tian; Yost, David
- Date
- 2018
- Type
- Text; Book chapter
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/182630
- Identifier
- vital:16185
- Identifier
-
https://doi.org/10.1007/978-3-319-72299-3_7
- Identifier
- ISBN:2523-3041
- Abstract
- While faces of a polytope form a well structured lattice, in which faces of each possible dimension are present, this is not true for general compact convex sets. We address the question of what dimensional patterns are possible for the faces of general closed convex sets. We show that for any finite sequence of positive integers there exist compact convex sets which only have extreme points and faces with dimensions from this prescribed sequence. We also discuss another approach to dimensionality, considering the dimension of the union of all faces of the same dimension. We show that the questions arising from this approach are highly nontrivial and give examples of convex sets for which the sets of extreme points have fractal dimension.
- Publisher
- Springer International Publishing
- Relation
- 2016 Matrix Annals p. 167-175
- Rights
- All metadata describing materials held in, or linked to, the repository is freely available under a CC0 licence
- Rights
- Copyright @ Springer International Publishing AG, part of Springer Nature 2018
- Rights
- Open Access
- Full Text
- Reviewed
- Hits: 223
- Visitors: 264
- Downloads: 59
| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
| View Details Download | SOURCE2 | Accepted version | 774 KB | Adobe Acrobat PDF | View Details Download |