The completely distributive lattice of machine invariant sets of infnite words

2007 ◽  
Vol 27 (1) ◽  
pp. 109
Author(s):  
A. Belovs ◽  
J. Buls
Keyword(s):  
Distributive Lattice ◽  
Invariant Sets ◽  
Completely Distributive ◽  
Completely Distributive Lattice

Metrizability Conditions for Completely Distributive Lattices

1983 ◽  
Vol 26 (4) ◽  
pp. 446-453
Author(s):  
G. Gierz ◽  
J. D. Lawson ◽  
A. R. Stralka
Keyword(s):  
Distributive Lattice ◽  
Essential Extension ◽  
Distributive Lattices ◽  
Interval Topology ◽  
Completely Distributive ◽  
Countable Chain ◽  
Completely Distributive Lattice

AbstractA lattice is said to be essentially metrizable if it is an essential extension of a countable lattice. The main result of this paper is that for a completely distributive lattice the following conditions are equivalent: (1) the interval topology on L is metrizable, (2) L is essentially metrizable, (3) L has a doubly ordergenerating sublattice, (4) L is an essential extension of a countable chain.

scholarly journals Essential completions of distributive lattices

1985 ◽  
Vol 32 (3) ◽  
pp. 361-374 ◽  
Author(s):  
Gerhard Gierz ◽  
Albert R. Stralka
Keyword(s):  
Distributive Lattice ◽  
Salient Feature ◽  
Distributive Lattices ◽  
Compact Topological Space ◽  
Completely Distributive ◽  
Completion Process ◽  
The One ◽  
One Point Compactification ◽  
Essential Completion ◽  
Completely Distributive Lattice

The salient feature of the essential completion process is that for most common distributive lattices it will yield a completely distributive lattice. In this note it is shown that for those distributive lattices which have at least one completely distributive essential extension the essential completion is minimal among the completions by infinitely distributive lattices. Thus in its setting the essential completion of a distributive lattice behaves in much the some way as the one-point compactification of locally compact topological space does in its setting.

Fuzzy generalized convex spaces

2020 ◽  
Vol 39 (3) ◽  
pp. 3907-3919
Author(s):  
Xiu-Yun Wu
Keyword(s):  
Distributive Lattice ◽  
Convex Space ◽  
Completely Distributive ◽  
Generalized Convex Space ◽  
Completely Distributive Lattice ◽  
Convex Spaces

On completely distributive lattice, the notion of fuzzy generalized convex space is introduced. It can be characterized by many means including fuzzy generalized hull space, fuzzy generalized restricted hull space, fuzzy generalized convexly enclosed relation space and fuzzy generalized derived hull space.

scholarly journals Measurement of Countable Compactness and Lindelöf Property in RL -Fuzzy Topological Spaces

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Xiongwei Zhang ◽  
Ibtesam Alshammari ◽  
A. Ghareeb
Keyword(s):  
Distributive Lattice ◽  
Topological Spaces ◽  
Fuzzy Topology ◽  
Implication Operator ◽  
Completely Distributive ◽  
Countable Compactness ◽  
Definition Of ◽  
Fuzzy Topological Spaces ◽  
Completely Distributive Lattice ◽  
Special Case

Based on the concepts of pseudocomplement of L -subsets and the implication operator where L is a completely distributive lattice with order-reversing involution, the definition of countable RL -fuzzy compactness degree and the Lindelöf property degree of an L -subset in RL -fuzzy topology are introduced and characterized. Since L -fuzzy topology in the sense of Kubiak and Šostak is a special case of RL -fuzzy topology, the degrees of RL -fuzzy compactness and the Lindelöf property are generalizations of the corresponding degrees in L -fuzzy topology.

Distributive and completely distributive lattice extensions of ordered sets

2018 ◽  
Vol 28 (03) ◽  
pp. 521-541 ◽  
Author(s):  
W. Morton ◽  
C. J. van Alten
Keyword(s):  
Distributive Lattice ◽  
Canonical Extension ◽  
Separation Property ◽  
Distributive Lattices ◽  
Ordered Sets ◽  
Prime Filter ◽  
Completely Distributive ◽  
Canonical Extensions ◽  
Completely Distributive Lattice

It is known that a poset can be embedded into a distributive lattice if, and only if, it satisfies the prime filter separation property. We describe here a class of “prime filter completions” for posets with the prime filter separation property that are completely distributive lattices generated by the poset and preserve existing finite meets and joins. The free completely distributive lattice generated by a poset can be obtained through such a prime filter completion. We also show that every completely distributive completion of a poset with the prime filter separation property is representable as a canonical extension of the poset with respect to some set of filters and ideals. The connections between the prime filter completions and canonical extensions are described and yield the following corollary: the canonical extension of any distributive lattice is the free completely distributive lattice generated by the lattice. A construction that is a variant of the prime filter completion is given that can be used to obtain the free distributive lattice generated by a poset. In addition, it is shown that every distributive lattice extension of the poset can be represented by such a construction. Finally, we show that a poset with the prime filter separation property and the free distributive lattice generated by it generates the same free completely distributive lattice.

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