تقرير
Lattice Diversities
| العنوان: | Lattice Diversities |
|---|---|
| المؤلفون: | Bryant, David, Felipe, Raúl, Toledo-Acosta, Mauricio, Tupper, Paul |
| سنة النشر: | 2020 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Metric Geometry, 06B75 |
| الوصف: | Diversities are a generalization of metric spaces, where instead of the non-negative function being defined on pairs of points, it is defined on arbitrary finite sets of points. Diversities have a well-developed theory. This includes the concept of a diversity tight span that extends the metric tight span in a natural way. Here we explore the generalization of diversities to lattices. Instead of defining diversities on finite subsets of a set we consider diversities defined on members of an arbitrary lattice (with a 0). We show that many of the basic properties of diversities continue to hold. However, the natural map from a lattice diversity to its tight span is not a lattice homomorphism, preventing the development of a complete tight span theory as in the metric and diversity cases. Comment: 18 pages, 4 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2010.11442 |
| رقم الأكسشن: | edsarx.2010.11442 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |