Lattice-valued preordered sets as lattice-valued topological
systems

J 2015

Lattice-valued preordered sets as lattice-valued topological systems

DENNISTON, Jeffrey; Austin MELTON; Stephen RODABAUGH a Sergejs SOLOVJOVS

Základní údaje

Originální název

Lattice-valued preordered sets as lattice-valued topological systems

Autoři

DENNISTON, Jeffrey (840 Spojené státy); Austin MELTON (840 Spojené státy); Stephen RODABAUGH (840 Spojené státy) a Sergejs SOLOVJOVS (428 Lotyšsko, garant, domácí)

Vydání

Fuzzy Sets and Systems, 2015, 0165-0114

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Nizozemské království

Utajení

není předmětem státního či obchodního tajemství

Impakt faktor

Impact factor: 2.098

Kód RIV

RIV/00216224:14310/15:00082330

Organizační jednotka

Přírodovědecká fakulta

DOI

http://dx.doi.org/10.1016/j.fss.2014.04.022

UT WoS

000345440400009

EID Scopus

2-s2.0-84912150700

Klíčová slova anglicky

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

Štítky

AKR, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 7. 4. 2016 08:35, Ing. Andrea Mikešková

Anotace

V originále

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.

Návaznosti

EE2.3.20.0051, projekt VaV

Název: Algebraické metody v kvantové logice

Citovat

DENNISTON, Jeffrey; Austin MELTON; Stephen RODABAUGH a Sergejs SOLOVJOVS. Lattice-valued preordered sets as lattice-valued topological systems. Fuzzy Sets and Systems. 2015, roč. 259, January, s. 89-110. ISSN 0165-0114. Dostupné z: https://dx.doi.org/10.1016/j.fss.2014.04.022.

@article{1219960,
   author = {Denniston, Jeffrey and Melton, Austin and Rodabaugh, Stephen and Solovjovs, Sergejs},
   article_number = {January},
   doi = {http://dx.doi.org/10.1016/j.fss.2014.04.022},
   keywords = {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},
   language = {eng},
   issn = {0165-0114},
   journal = {Fuzzy Sets and Systems},
   title = {Lattice-valued preordered sets as lattice-valued topological systems},
   volume = {259},
   year = {2015}
}

TY  - JOUR
ID  - 1219960
AU  - Denniston, Jeffrey - Melton, Austin - Rodabaugh, Stephen - Solovjovs, Sergejs
PY  - 2015
TI  - Lattice-valued preordered sets as lattice-valued topological systems
JF  - Fuzzy Sets and Systems
VL  - 259
IS  - January
SP  - 89-110
EP  - 89-110
SN  - 01650114
KW  - Adjoint functor
KW  - Alexandroff topology
KW  - Coreflective subcategory
KW  - (Lattice-valued) preordered set
KW  - (Lattice-valued) topological space
KW  - (Lattice-valued) topological system
KW  - Locale
KW  - Quasi-pseudo-metric space
KW  - Spatialization procedure
N2  - 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.
ER  -

DENNISTON, Jeffrey; Austin MELTON; Stephen RODABAUGH a Sergejs SOLOVJOVS. Lattice-valued preordered sets as lattice-valued topological systems. \textit{Fuzzy Sets and Systems}. 2015, roč.~259, January, s.~89-110. ISSN~0165-0114. Dostupné z: https://dx.doi.org/10.1016/j.fss.2014.04.022.

Přehled o publikaci