Lattice-valued preordered sets as lattice-valued topological systems

被引：5

作者：

Denniston, Jeffrey T. ^{[1
]}

Melton, Austin ^{[2
]}

Rodabaugh, Stephen E. ^{[3
]}

Solovyov, Sergey A. ^{[4
]}

机构：

[1] Kent State Univ, Dept Math Sci, Kent, OH 44242 USA

[2] Kent State Univ, Dept Comp Sci & Math Sci, Kent, OH 44242 USA

[3] Youngstown State Univ, Coll Sci Technol Engn Math STEM, Youngstown, OH 44555 USA

[4] Masaryk Univ, Fac Sci, Dept Math & Stat, CS-61137 Brno, Czech Republic

来源：

FUZZY SETS AND SYSTEMS | 2015年 / 259卷

关键词：

Adjoint functor; Alexandroff topology; Coreflective subcategory; (Lattice-valued) preordered set; (Lattice-valued) topological space; (Lattice-valued) topological system; Locale; Quasi-pseudo-metric space; Spatialization procedure; Specialization preorder; Topological category; (Variable-basis) pointfree topology; FUZZY; FOUNDATIONS; ALGEBRA;

D O I：

10.1016/j.fss.2014.04.022

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

This paper provides variable-basis lattice-valued analogues of the well-known results that the construct Prost of preordered sets, firstly, is concretely isomorphic to a full concretely coreflective subcategory of the category Top of topological spaces (which employs the concept of the dual of the specialization preorder), and, secondly, is (non-concretely) isomorphic to a full coreflective subcategory of the category TopSys of topological systems of S. Vickers (which employs the spatialization procedure for topological systems) Dualizing these results, one arrives at the similar properties of quasi-pseudo-metric spaces built over locales. (C) 2014 Elsevier B.V. All rights reserved.

引用

页码：89 / 110

页数：22

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