Affiliation:
1. Faculty of Science, Jiangxi University of Science and Technology , Ganzhou , Jiangxi 341000 , China
2. Fujian key Laboratory of Granular Computing and Applications, Minnan Normal University , Zhangzhou , Fujian 363000 , China
Abstract
Abstract
In this paper, we define the concepts of strongly regular relation, finitely strongly regular relation, and generalized finitely strongly regular relation, and get the relational representations of strongly algebraic, hyperalgebraic, and quasi-hyperalgebraic lattices. The main results are as follows: (1) a binary relation
ρ
:
X
⇀
Y
\rho :X\hspace{0.33em}\rightharpoonup \hspace{0.33em}Y
is strongly regular if and only if the complete lattice
(
Φ
ρ
(
X
)
,
⊆
)
\left({\Phi }_{\rho }\left(X),\subseteq )
is a strongly algebraic lattice; (2) a binary relation
ρ
:
X
⇀
Y
\rho :X\hspace{0.33em}\rightharpoonup \hspace{0.33em}Y
is finitely strongly regular if and only if
(
Φ
ρ
(
X
)
,
⊆
)
\left({\Phi }_{\rho }\left(X),\subseteq )
is a hyperalgebraic lattice if and only if the finite extension of
ρ
\rho
is strongly regular; and (3) a binary relation
ρ
:
X
⇀
Y
\rho :X\hspace{0.33em}\rightharpoonup \hspace{0.33em}Y
is generalized finitely strongly regular if and only if
(
Φ
ρ
(
X
)
,
⊆
)
\left({\Phi }_{\rho }\left(X),\subseteq )
is a quasi-hyperalgebraic lattice if and only if
(
Φ
ρ
(
X
)
,
⊆
)
\left({\Phi }_{\rho }\left(X),\subseteq )
equipped with the interval topology is a Priestley space.
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献