Continuous and Completely Distributive Lattices

2014 ◽  
pp. 5-53
Author(s):  
Klaus Keimel ◽  
Jimmie Lawson
Keyword(s):  
Distributive Lattices ◽  
Completely Distributive

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 Groupoidal completely distributive lattices

1999 ◽  
Vol 143 (1-3) ◽  
pp. 339-350 ◽  
Author(s):  
M.C. Pedicchio ◽  
R.J. Wood
Keyword(s):  
Distributive Lattices ◽  
Completely Distributive

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.

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