NETS AND SEPARATED S-POSETS

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

کلیدواژه ها:

S-poset ، Separated S-poset ، Separation axioms