On two types of closure operators associated with networks

Abstract

Binary relation plays a prominent role in the study of network structures. Since network structures are discrete system, topological techniques cannot be utilized to study the system. Rather, the concept of closed sets defined in closure spaces involving a closure operator is used in such types of studies. Recently, Šlapal and Pfaltz studied network structures by using foresets as defined in the Closure spaces via relation. In this paper, two types of closure operators via relations are taken into consideration to verify some results associated with networks. In one case, the relation is binary whereas in the other case the relation is reflexive and symmetric. The situation when a network structure is discrete/indiscrete is investigated. Further, a situation in which a set is closed in a tree-like network structure is obtained and examples in support are provided.