nets and separated s-posets

nets, useful topological tools, used to generalize certainconcepts that may only be general enough in the context of metricspaces. in this work we introduce this concept in an $s$-poset, aposet with an action of a posemigroup $s$ on it whichis a very useful structure in computer sciences and interestingfor mathematicians, and give the the concept of $s$-net. using $s$-nets and itsconvergency we also give some characterizations of separated$s$-posets.also, introducing the net-closure operators, we investigatethe counterparts of topological separation axioms on $s$-posetsand study their relation to separated $s$-posets.