A visual approach to test lattices

Gábor Czédli

Displaying similar documents to “A visual approach to test lattices”

Algebraic lattices are complete sublattices of the clone lattice over an infinite set

Michael Pinsker (2007)

Fundamenta Mathematicae

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The clone lattice Cl(X) over an infinite set X is a complete algebraic lattice with $2^{| X |}$ compact elements. We show that every algebraic lattice with at most $2^{| X |}$ compact elements is a complete sublattice of Cl(X).

The Banach lattice C[0,1] is super d-rigid

Y. A. Abramovich, A. K. Kitover (2003)

Studia Mathematica

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The following properties of C[0,1] are proved here. Let T: C[0,1] → Y be a disjointness preserving bijection onto an arbitrary vector lattice Y. Then the inverse operator $T^{- 1}$ is also disjointness preserving, the operator T is regular, and the vector lattice Y is order isomorphic to C[0,1]. In particular if Y is a normed lattice, then T is also automatically norm continuous. A major step needed for proving these properties is provided by Theorem 3.1 asserting that T satisfies some technical...

Lattice-inadmissible incidence structures

Frantisek Machala, Vladimír Slezák (2004)

Discussiones Mathematicae - General Algebra and Applications

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Join-independent and meet-independent sets in complete lattices were defined in [6]. According to [6], to each complete lattice (L,≤) and a cardinal number p one can assign (in a unique way) an incidence structure $J_{L}^{p}$ of independent sets of (L,≤). In this paper some lattice-inadmissible incidence structures are founded, i.e. such incidence structures that are not isomorphic to any incidence structure $J_{L}^{p}$ .

Congruence lattices of intransitive G-Sets and flat M-Sets

Steve Seif (2013)

Commentationes Mathematicae Universitatis Carolinae

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An M-Set is a unary algebra $〈 X, M 〉$ whose set $M$ of operations is a monoid of transformations of $X$ ; $〈 X, M 〉$ is a G-Set if $M$ is a group. A lattice $L$ is said to be represented by an M-Set $〈 X, M 〉$ if the congruence lattice of $〈 X, M 〉$ is isomorphic to $L$ . Given an algebraic lattice $L$ , an invariant $Π (L)$ is introduced here. $Π (L)$ provides substantial information about properties common to all representations of $L$ by intransitive G-Sets. $Π (L)$ is a sublattice of $L$ (possibly isomorphic to the trivial lattice), a $Π$ -product lattice....

A T-partial order obtained from T-norms

Funda Karaçal, M. Nesibe Kesicioğlu (2011)

Kybernetika

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A partial order on a bounded lattice $L$ is called t-order if it is defined by means of the t-norm on $L$ . It is obtained that for a t-norm on a bounded lattice $L$ the relation $a ⪯_{T} b$ iff $a = T (x, b)$ for some $x \in L$ is a partial order. The goal of the paper is to determine some conditions such that the new partial order induces a bounded lattice on the subset of all idempotent elements of $L$ and a complete lattice on the subset $A$ of all elements of $L$ which are the supremum of a subset of atoms.