Compact pospaces
Venu G. Menon (2003)
Commentationes Mathematicae Universitatis Carolinae
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Posets with property DINT which are compact pospaces with respect to the interval topologies are characterized.
Venu G. Menon (2003)
Commentationes Mathematicae Universitatis Carolinae
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Posets with property DINT which are compact pospaces with respect to the interval topologies are characterized.
Menon, Venu G. (2008)
International Journal of Mathematics and Mathematical Sciences
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Marcel Erné (2013)
Mathematica Bohemica
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It is known that for a nonempty topological space and a nonsingleton complete lattice endowed with the Scott topology, the partially ordered set of all continuous functions from into is a continuous lattice if and only if both and the open set lattice are continuous lattices. This result extends to certain classes of -distributive lattices, where is a subset system replacing the system of all directed subsets (for which the -distributive complete lattices are just...
Ivan Chajda (2012)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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We show that every pseudocomplemented poset can be equivalently expressed as a certain algebra where the operation of pseudocomplementation can be characterized by means of remaining two operations which are binary and nullary. Similar characterization is presented for Stone posets.
Alireza Vaezi, Vilas Kharat (2017)
Mathematica Bohemica
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We introduce statisch pairs in atomistic posets and study its relationships with some known concepts in posets such as biatomic and dual modular pairs, perspectivity and subspaces of atom space of an atomistic poset. We generalize the notion of exchange property in posets and with the help of it we prove the equivalence of dual modular, biatomic and statisch pairs in atomistic posets. Also, we prove that the set of all finite elements of a statisch poset with such property forms an ideal....
Zoltán Ésik, Zoltán L. Németh (2005)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
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A -labeled -poset is an (at most) countable set, labeled in the set , equipped with partial orders. The collection of all -labeled -posets is naturally equipped with binary product operations and -ary product operations. Moreover, the -ary product operations give rise to -power operations. We show that those -labeled -posets that can be generated from the singletons by the binary and -ary product operations form the free algebra on in...