In the present paper, we introduce and study the continuity and some properties for a set equipped with a
transitive binary relation which we call t-set. Also, we give a characterization of a continuous directed complete posets via continuous t-sets. Furthermore, some properties of algebraic t-sets are considered. Our work is inspired by the slogan: "Order theory is the study of transitive relations" due to Abramsky and Jung [1]. The corresponding results of our results due to Nino-Salcedo [8], Heckmann [4] and Zhang [11] are generalized.