Scott-topology based on transitive binary relation

Document Type : Research Paper

Authors

1 Department of Mathematics Faculty of Science, Assiut University, 71516 EGYPT

2 Department of Mathematics, Faculty of Science, New Valley University, EGYPT

Abstract

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.

Keywords


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  • Receive Date: 09 December 2021
  • Revise Date: 10 April 2022
  • Accept Date: 24 April 2022
  • First Publish Date: 24 April 2022