Fractoconvex structures
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2017
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| Accesso online: | |
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| _version_ | 1866913470005379072 |
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| author | Dulliev, Aidar |
| author_facet | Dulliev, Aidar |
| contents | We define a new structure on a space endowed with convexities, and call it a fractoconvex structure (or, a space with fractoconvexity). We introduce two operations on a set of fractoconvexities and in a special case we show that they satisfy the laws for a distributive lattice. We establish a connection between fractoconvex sets and convex sets using the concept of independent convexities, based on the possibility of representing a fractoconvex set as the intersection of its convex hulls. Finally, we consider some examples of fractoconvexities on the 2-sphere and on $\mathbb Z$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1710_04263 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Fractoconvex structures Dulliev, Aidar General Mathematics 52A01, 52A30, 52A99 We define a new structure on a space endowed with convexities, and call it a fractoconvex structure (or, a space with fractoconvexity). We introduce two operations on a set of fractoconvexities and in a special case we show that they satisfy the laws for a distributive lattice. We establish a connection between fractoconvex sets and convex sets using the concept of independent convexities, based on the possibility of representing a fractoconvex set as the intersection of its convex hulls. Finally, we consider some examples of fractoconvexities on the 2-sphere and on $\mathbb Z$. |
| title | Fractoconvex structures |
| topic | General Mathematics 52A01, 52A30, 52A99 |
| url | https://arxiv.org/abs/1710.04263 |