
Summary: 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.
Separated $S$-poset, \(S\)-poset, Representation of semigroups; actions of semigroups on sets, separated \(S\)-poset, Separation axioms, Partial orders, general, Lower separation axioms (\(T_0\)--\(T_3\), etc.), separation axioms, QA1-939, Ordered semigroups and monoids, Connections of semigroups with homological algebra and category theory, Mathematics, $S$-poset
Separated $S$-poset, \(S\)-poset, Representation of semigroups; actions of semigroups on sets, separated \(S\)-poset, Separation axioms, Partial orders, general, Lower separation axioms (\(T_0\)--\(T_3\), etc.), separation axioms, QA1-939, Ordered semigroups and monoids, Connections of semigroups with homological algebra and category theory, Mathematics, $S$-poset
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