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Article . 2013
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Article . 2013
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Article . 2013
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NETS AND SEPARATED S-POSETS

Nets and separated \(S\)-posets
Authors: Haddadi, Mahdieh;

NETS AND SEPARATED S-POSETS

Abstract

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.

Related Organizations
Keywords

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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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average