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arXiv · 1710.04263

Fractoconvex structures

Aidar Dulliev
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Abstract

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 $\mathbb Z$.

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Aidar Dulliev. 2017-10-11. Fractoconvex structures. https://arxiv.org/abs/1710.04263

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