TY - JOUR ID - 3266 TI - Scott-topology based on transitive binary relation JO - Journal of Mahani Mathematical Research JA - JMMR LA - en SN - 2251-7952 AU - Sayed, Osama Rashed AU - Sayed, Nabil Hassan AD - Department of Mathematics Faculty of Science, Assiut University, 71516 EGYPT AD - Department of Mathematics, Faculty of Science, New Valley University, EGYPT Y1 - 2022 PY - 2022 VL - 11 IS - 2 SP - 127 EP - 139 KW - Scott-topology KW - Directed topology KW - t-set DO - 10.22103/jmmrc.2022.18653.1181 N2 - In the study of partially ordered sets, topologies such as Scott-topology have shown to be of paramount importance. In order to have analogous topology-like tools in the more general setting of quantitative domains, we introduce a method to construct Scotttopology on a set equipped with a transitive binary relation which we call t-set. As an application of this result there is a Scott-topology associated to any topology induced by its specialization pre-ordered relation. Some relations between this topology and the original topology are investigated. UR - https://jmmrc.uk.ac.ir/article_3266.html L1 - https://jmmrc.uk.ac.ir/article_3266_9133f5d1226b4c713b7df37dc1f682a1.pdf ER -