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A separoid is a symmetric relation $† \subset (\binom{2^{S}}{2})$ defined on disjoint pairs of subsets of a given set $S$ such that it is closed as a filter in the canonical partial order induced by the inclusion (i.e., $A † B ⪯ A^{'} † B^{'} \Leftrightarrow A \subseteq A^{'}$ and $B \subseteq B^{'}$ ). We introduce the notion of homomorphism as a map which preserve the so-called “minimal Radon partitions” and show that separoids, endowed with these maps, admits an embedding from the category of all finite graphs. This proves that separoids constitute a countable universal partial order. Furthermore,...

Upper and Lower Bounds in Relator Spaces

Száz, Árpád (2003)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 06A06, 54E15An ordered pair X(R) = ( X, R ) consisting of a nonvoid set X and a nonvoid family R of binary relations on X is called a relator space. Relator spaces are straightforward generalizations not only of uniform spaces, but also of ordered sets. Therefore, in a relator space we can naturally define not only some topological notions, but also some order theoretic ones. It turns out that these two, apparently quite different, types of notions are closely...

Varieties of idempotent groupoids with small clones

J. Gałuszka (1999)

Colloquium Mathematicae

We give an equational description of all idempotent groupoids with at most three essentially n-ary term operations.

Vector-valued fuzzy measures on fuzzy quantum posets

Le Ba Long (1993)

Mathematica Slovaca

Venn diagrams and symmetric chain decompositions in the Boolean lattice.

Griggs, Jerrold, Killian, Charles E., Savage, Carla D. (2004)

The Electronic Journal of Combinatorics [electronic only]

Verallgemeinerte Verbände mit innerer Verbandsstruktur

H. Kröger (1981)

Matematički Vesnik

Verbände von Kernen isotoner Abbildungen

Teo Sturm (1972)

Czechoslovak Mathematical Journal

Verbandstheoretische Eigenschaften von Sprachen. II

Josef Dalík (1977)

Archivum Mathematicum

V-Free Products of Hopfian Lattices.

M.E. Adams, J. Sichler (1976)

Mathematische Zeitschrift

Visibility Graphs of Staircase Polygons and the Weak Bruhat Order, I: from Visibility Graphs to Maximal Chains.

K. Kumar, J. Abello, O. Egecioglu (1995)

Discrete & computational geometry

Weak chain-completeness and fixed point property for pseudo-ordered sets

S. Parameshwara Bhatta (2005)

Czechoslovak Mathematical Journal

In this paper the notion of weak chain-completeness is introduced for pseudo-ordered sets as an extension of the notion of chain-completeness of posets (see [3]) and it is shown that every isotone map of a weakly chain-complete pseudo-ordered set into itself has a least fixed point.

Weak homomorphisms in implication algebra

Ivan Chajda (1990)

Časopis pro pěstování matematiky

Weak incidence algebra and maximal ring of quotients.

Singh, Surjeet, Al-Thukair, Fawzi (2004)

International Journal of Mathematics and Mathematical Sciences

Weak product decompositions of partially ordered sets

J. Jakubík (1972)

Colloquium Mathematicae

Weighted $w$ -core inverses in rings

Liyun Wu, Huihui Zhu (2023)

Czechoslovak Mathematical Journal

Let $R$ be a unital $*$ -ring. For any $a, s, t, v, w \in R$ we define the weighted $w$ -core inverse and the weighted dual $s$ -core inverse, extending the $w$ -core inverse and the dual $s$ -core inverse, respectively. An element $a \in R$ has a weighted $w$ -core inverse with the weight $v$ if there exists some $x \in R$ such that $a w x v x = x$ , $x v a w a = a$ and ${(a w x)}^{*} = a w x$ . Dually, an element $a \in R$ has a weighted dual $s$ -core inverse with the weight $t$ if there exists some $y \in R$ such that $y t y s a = y$ , $a s a t y = a$ and ${(y s a)}^{*} = y s a$ . Several characterizations of weighted $w$ -core invertible and weighted dual $s$ -core invertible...

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