The present paper is devoted to study some completeness properties of transitive binary relational set, i.e., a set together with a transitive binary relation (so called t-set). We hope that the results of our paper will be a starting  point for a sufficiently general but simple theory of objects that are suitable for modelling various aspects of  computation and useful in modern applications of domain theory to general topology and mathematical analysis.

http://dx.doi.org/10.18642/jmsaa_7100122266

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