Displaying similar documents to “The hyperbola x y = N

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

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

Studia Mathematica

Similarity:

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...

On the special context of independent sets

Vladimír Slezák (2001)

Discussiones Mathematicae - General Algebra and Applications

Similarity:

In this paper the context of independent sets J L p is assigned to the complete lattice (P(M),⊆) of all subsets of a non-empty set M. Some properties of this context, especially the irreducibility and the span, are investigated.

A visual approach to test lattices

Gábor Czédli (2009)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Similarity:

Let p be a k -ary lattice term. A k -pointed lattice L = ( L ; , , d 1 , ... , d k ) will be called a p -lattice (or a test lattice if p is not specified), if ( L ; , ) is generated by { d 1 , ... , d k } and, in addition, for any k -ary lattice term q satisfying p ( d 1 , ... , d k ) q ( d 1 , ... , d k ) in L , the lattice identity p q holds in all lattices. In an elementary visual way, we construct a finite p -lattice L ( p ) for each p . If p is a canonical lattice term, then L ( p ) coincides with the optimal p -lattice of Freese, Ježek and Nation [Freese,...

A T-partial order obtained from T-norms

Funda Karaçal, M. Nesibe Kesicioğlu (2011)

Kybernetika

Similarity:

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 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.

On extensions of orthosymmetric lattice bimorphisms

Mohamed Ali Toumi (2013)

Mathematica Bohemica

Similarity:

In the paper we prove that every orthosymmetric lattice bilinear map on the cartesian product of a vector lattice with itself can be extended to an orthosymmetric lattice bilinear map on the cartesian product of the Dedekind completion with itself. The main tool used in our proof is the technique associated with extension to a vector subspace generated by adjoining one element. As an application, we prove that if ( A , * ) is a commutative d -algebra and A 𝔡 its Dedekind completion, then, A 𝔡 can...

Polynomial growth of sumsets in abelian semigroups

Melvyn B. Nathanson, Imre Z. Ruzsa (2002)

Journal de théorie des nombres de Bordeaux

Similarity:

Let S be an abelian semigroup, and A a finite subset of S . The sumset h A consists of all sums of h elements of A , with repetitions allowed. Let | h A | denote the cardinality of h A . Elementary lattice point arguments are used to prove that an arbitrary abelian semigroup has polynomial growth, that is, there exists a polynomial p ( t ) such that | h A | = p ( h ) for all sufficiently large h . Lattice point counting is also used to prove that sumsets of the form h 1 A 1 + + h r A r have multivariate polynomial growth.

Lattice-inadmissible incidence structures

Frantisek Machala, Vladimír Slezák (2004)

Discussiones Mathematicae - General Algebra and Applications

Similarity:

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 .