Some betweenness relation topologies induced by simplicial complexes. (English) Zbl 1513.54005
Summary: This article aims to create an approximation space from any simplicial complex by representing a finite simplicial complex as a union of its components. These components are arranged into levels beginning with the highest-dimensional simplices. The universal set of the approximation space is comprised of a collection of all vertices, edges, faces, and tetrahedrons, and so on. Moreover, new types of upper and lower approximations in terms of a betweenness relation will be defined. A betweenness relation means that an element lies between two elements: an upper bound and a lower bound. In this work, based on H.-P. Zhang’s et al. [Topology Appl. 258, 100–114 (2019; Zbl 1412.06001)] concept, a betweenness relation on any simplicial complex, which produces a set of order relations, is established and some of its topologies are studied.
MSC:
| 54A05 | Topological spaces and generalizations (closure spaces, etc.) |
| 54F05 | Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces |
| 06A06 | Partial orders, general |
| 60L20 | Rough paths |
| 92C50 | Medical applications (general) |
Keywords:
simplicial complexes; approximation spaces; order relation; topological spaces; betweenness relationCitations:
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