Abstract
In this work we naturally put forth an open question whether one may construct a scott-topology on transitive binary relational sets (so called TRS). We prove that a TRS gives rise to several natural topologies defined in terms of the given TRS structure. Mainly, we consider directed topologies and scott topologies on TRS and their interactions with the continuity property of TRS. Most of our results are generalizations of corresponding results in references as we will illustrate. Sometimes we need pre-ordered sets instead of TRS.
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