Results 261 to 270 of about 87,663 (288)

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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Splittability for Partially Ordered Sets

Order, 2000
This paper deals with an extension of the notion of splittability (cleavability) of topological spaces, introduced by Arkhangel'skij (1985), to partially ordered sets [\textit{D. J. Marron} and \textit{T. B. M. McMaster}, Math. Proc. R. Ir. Acad. 99A, 189-194 (1999; Zbl 0966.06002)] as follows: If \(A\) is a subset of a poset \(X\), we say that \(X ...
Hanna, A. J., McMaster, T. B. M.
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Decompositions of Partially Ordered Sets

Order, 2000
In a previous paper [J. Comb. Theory, Ser. A 89, 77-104 (2000; Zbl 0959.52010)] the authors characterized the cone of linear inequalities holding for the flag \(f\)-vectors of all graded posets of a given rank. In the paper under review they give a description of the cone of flag \(f\)-vectors of planar graded posets. The proof includes a special chain-
Billera, Louis J., Hetyei, Gábor
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Partially Ordered Sets

1988
The present chapter gives some mathematical theory of partially ordered sets. Referring to the appendix on terminology, we recall that a partially ordered set is a pair (X, ≺) where ≺ is an irreflexive and transitive relation on X. We shall not immediately give the interpretation of the elements of X.
Eike Best, César C. Fernández
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Completions of Partially Ordered Sets

SIAM Journal on Computing, 1982
We show, for any subset system Z (as defined in Wright, Wagner, and Thatcher, T.C.S. 7 (1978), pp. 57–77) and any order preserving map $f:Q \to P$ of posets, the existence of a universal map $u_f :P \to P_f $ where $P_f $ is Z-complete and $u_f f$ is Z-continuous. This generalizes to arbitrary subset systems the result of Markowsky (T.C.S. 4 (1977), pp.
Banaschewski, Bernhard, Nelson, Evelyn
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Homomorphism-Homogeneous Partially Ordered Sets

Order, 2007
A homomorphism between posets \((A,\leq)\) and \((B,\leq)\) is a map preserving the ordering \(\leq\). A poset \(P\) is called homomorphism-homogeneous if every homomorphism \(A\to B\) of sub-posets \(A,B\subset P\) can be extended to a homomorphism \(P\to P\).
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P-Faithful Partially Ordered Sets

Ukrainian Mathematical Journal, 2002
Summary: We prove a theorem that describes \(P\)-faithful partially ordered sets.
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Path‐Connected Partially Ordered Sets

Studies in Applied Mathematics, 1979
The graph of a partially ordered set (X, ⩽) has X as its set of vertices and (x,y) is an edge if and only if x covers y or y covers x. The poset is path‐connected if its graph is connected. Two integer‐valued metrics, distance and fence, are defined for path‐connected posets.
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Rough Sets in Partially Ordered Sets

2010 IEEE International Conference on Granular Computing, 2010
It is well-known to us that the Pawlak’s rough set theory, an effective tool to deal with uncertainty and granularity in information systems, is based on equivalence relation. However, in some situations, those conditions of equivalence relation are hardly met.
Kai Li, William Zhu, Jianguo Tang
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Ordering Uniform Completions of Partially Ordered Sets

Canadian Journal of Mathematics, 1974
Let (P, ) be a (nearly) uniform ordered space. Let (P, ) be the uniform completion of (P, ) at . Several partial orders for P are introduced and discussed. One of these orders provides an adjoint to the functor which embeds the category of uniformly complete uniform ordered spaces in the category of uniform ordered spaces, both categories with ...
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