Strictly locally order affine complete lattices

Order ◽  
1993 ◽  
Vol 10 (3) ◽  
pp. 261-270 ◽  
Author(s):  
Kalle Kaarli ◽  
Karin T�ht
Keyword(s):  
Complete Lattices ◽  
Affine Complete

Q-orders with no unit on Q

2021 ◽  
pp. 1-8
Author(s):  
Cheng-Jie Zhou ◽  
Wei Yao
Keyword(s):  
Ordered Sets ◽  
Complete Lattices ◽  
Definition Of ◽  
Self Adaptive

For a usual commutative quantale Q (does not necessarily have a unit), we propose a definition of Q-ordered sets by introducing a kind of self-adaptive self-reflexivity. We study their completeness and the related Q-modules of complete lattices. The main result is that, the complete Q-ordered sets and the Q-modules of complete lattices are categorical isomorphic.

scholarly journals On complete objects in the category of T0 closure spaces

2003 ◽  
Vol 4 (1) ◽  
pp. 25 ◽  
Author(s):  
D. Deses ◽  
Eraldo Giuli ◽  
E. Lowen-Colebunders
Keyword(s):  
General Theory ◽  
Complete Lattices ◽  
Closure Spaces

<p>In this paper we present an example in the setting of closure spaces that fits in the general theory on “complete objects” as developed by G. C. L. Brümmer and E. Giuli. For V the class of epimorphic embeddings in the construct Cl<sub>0</sub> of T<sub>0</sub> closure spaces we prove that the class of V-injective objects is the unique firmly V-reflective subconstruct of Cl0. We present an internal characterization of the Vinjective objects as “complete” ones and it turns out that this notion of completeness, when applied to the topological setting is much stronger than sobriety. An external characterization of completeness is obtained making use of the well known natural correspondence of closures with complete lattices. We prove that the construct of complete T<sub>0</sub> closure spaces is dually equivalent to the category of complete lattices with maps preserving the top and arbitrary joins.</p>

Affine complete Stone algebras

1982 ◽  
Vol 39 (1-3) ◽  
pp. 169-174 ◽  
Author(s):  
R. Beazer
Keyword(s):  
Affine Complete
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