NETS AND SEPARATED S-POSETS

Nets, useful topological tools, used to generalize certain concepts that may only be general enough in the context of metric spaces. In this work we introduce this concept in an $S$-poset, a poset with an action of a posemigroup $S$ on it which is a very useful structure in computer sciences and interesting for mathematicians, and give the the concept of $S$-net. Using $S$-nets and its convergency we also give some characterizations of separated $S$-posets. Also, introducing the net-closure operators, we investigate the counterparts of topological separation axioms on $S$-posets and study their relation to separated $S$-posets.