Results 291 to 300 of about 665,193 (301)

Partially ordered sets

2015
Apples and oranges. Sometimes things are incomparable. For breakfast, I like granola better than gruel. I like it even better when my granola has fresh fruit on top. I also like a nice omelette better than gruel. But on any given day I cannot say whether I would prefer granola (with or without fruit) or an omelette. I am only able to partially order my
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Representation of partially ordered sets

Algebra Universalis, 1993
For a poset \((P,\leq)\) it is known that there is an ordering \((Q,\leq)\) and an isomorphism \(f\) between \(P\) and \(Q\) with either \[ (*) \quad f\Bigl( \bigwedge_{i\in S} a_ i \Bigr)= \bigwedge_{i\in S} f(a_ i) \qquad \text{ or } \qquad (**) \quad f\Bigl( \bigvee_{i\in S} a_ i \Bigr)= \bigvee_{i\in S} f(a_ i) \] for any finite indexing set \(S\).
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On the representation of partially ordered sets

Rendiconti del Circolo Matematico di Palermo, 1997
A poset \(P\) is left meet-distributive (LMD) if for all \(x,y,z\) of \(P\), if \(x\wedge(y\vee z)\) exists then also \((x\wedge y)\vee(x\wedge z)\) exists and they are equal. \(P\) is supremum-dense if each \(b\) of \(P\) is the join of all completely join-irreducible elements below \(b\).
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On the isomorphism of partially ordered sets

Algebra Universalis, 1971
As shown in [1], the existence of a one-to-one order preserving m a p p i n g f from a partially ordered set P onto a partially ordered set Q and a one-to-one order preserving mapping g from Q onto P does not imply that P and Q are isomorphic. Below we show that, under these conditions, P 'and Q are isomorphic provided each is a partially well ordered ...
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On subsets of a partially ordered set

Mathematical Proceedings of the Cambridge Philosophical Society, 1966
In this paper we discuss the structure of a partially ordered set X by studying in detail certain subsets of X.
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A Completion for Partially Ordered Sets

Journal of the London Mathematical Society, 1969
A completion is obtained by imbedding any partially ordered set into its (completely distributive, complete) lattice of lower semi-ideals.
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Representations of partially ordered sets [PDF]

Journal of Soviet Mathematics, 1975
A. V. Roiter, L. A. Nazarova
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Partially Ordered Set

2014
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The Cofinality of a Partially Ordered Set

Proceedings of the London Mathematical Society, 1983
Karel Prikry, E. C. Milner
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On the Dimension of Partially Ordered Sets

American Journal of Mathematics, 1948
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