Lattices of Irreducibly-derived Closed Sets | Zendy

Shuhua Su | Zendy; Qi Li | Zendy

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Lattices of Irreducibly-derived Closed Sets

Author(s) -

Shuhua Su,

Qi Li

Publication year - 2019

Publication title -

electronic notes in theoretical computer science

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.242

H-Index - 60

ISSN - 1571-0661

DOI - 10.1016/j.entcs.2019.07.026

Subject(s) - closed set , partially ordered set , cartesian product , cartesian closed category , lattice (music) , mathematics , cartesian coordinate system , combinatorics , star product , set (abstract data type) , topology (electrical circuits) , discrete mathematics , computer science , physics , geometry , acoustics , programming language

This paper pursues an investigation on the lattices of irreducibly-derived closed sets initiated by Zhao and Ho (2015). This time we focus the closed set lattice arising from the irreducibly-derived topology of Scott topology. For a poset X, the set Γ S I ( X ) of all irreducibly-derived Scott-closed sets (for short, SI-closed sets) ordered by inclusion forms a complete lattice. We introduce the notions of C S I -continuous posets and C S I -prealgebraic posets and study their properties. We also introduce the SI-dominated posets and show that for any two SI-dominated posets X and Y, X ≅ Y if and only if the SI-closed set lattices above them are isomorphic. At last, we show that the category of strong complete posets with SI-continuous maps is Cartesian-closed.

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