Search results for " set"

Bounded Bi-ideals and Linear Recurrence

2013

Bounded bi-ideals are a subclass of uniformly recurrent words. We introduce the notion of completely bounded bi-ideals by imposing a restriction on their generating base sequences. We prove that a bounded bi-ideal is linearly recurrent if and only if it is completely bounded.

Convex bodies and convexity on Grassmann cones

1962

Optimal Locations and Inner Products

1997

Abstract In a normed space X , we consider objective functions which depend on the distances between a variable point and the points of certain finite sets A . A point where such a function attains its minimum on X is generically called an optimal location. In this paper we obtain characterizations of inner product spaces with properties connecting optimal locations and the convex hull of A or barycenters of points of A with well chosen weights. We thus generalize several classical results about characterization of inner product spaces.

On norm attaining polynomials

2003

We show that for every Banach space X the set of 2-homogeneous continuous polynomials whose canonical extension to X∗∗ attain their norm is a dense subset of the space of all 2-homogeneous continuous polynomials P(2X).

Spaces of typen on partially ordered sets

1989

This paper contains a generalized approach to incidence geometry on partially ordered sets. A difference to the usual geometrical concepts is that points may have different size. Our main result states that a large class of spaces allows lattice theoretic characterizations. Especially, a generalized version of the Veblen-Young axiom of projective geometry has a lattice theoretic equivalent, called then-generation property (which is a generalization of the ‘Verbindungssatz’). Modularity and distributivity of a lattice of subspaces are reflected in the underlying space. Finally we give specializations and examples.

Completion of partially ordered sets

2007

Sigma-fragmentability and the property SLD in C(K) spaces

2009

Abstract We characterize two topological properties in Banach spaces of type C ( K ) , namely, being σ-fragmented by the norm metric and having a countable cover by sets of small local norm-diameter (briefly, the property norm-SLD). We apply our results to deduce that C p ( K ) is σ-fragmented by the norm metric when K belongs to a certain class of Rosenthal compacta as well as to characterize the property norm-SLD in C p ( K ) in case K is scattered.

Remarks on Partially Square Graphs, Hamiltonicity and Circumference

2001

Coding Partitions: Regularity, Maximality and Global Ambiguity

2007

The canonical coding partition of a set of words is the finest partition such that the words contained in at least two factorizations of a same sequence belong to a same class. In the case the set is not uniquely decipherable, it partitions the set into one unambiguous class and other parts that localize the ambiguities in the factorizations of finite sequences. We firstly prove that the canonical coding partition of a regular set contains a finite number of regular classes. We give an algorithm for computing this partition. We then investigate maximality conditions in a coding partition and we prove, in the regular case, the equivalence between two different notions of maximality. As an ap…

Centralizers of Parabolic Subgroups of Artin Groups of TypeAl,Bl, andDl

1997

Abstract Let ( A , Σ) be an Artin system of one of the types A l , B l , D l . For X  ⊆ Σ, we denote by A X the subgroup of A generated by X . Such a group is called a parabolic subgroup of ( A , Σ). Let A X be a parabolic subgroup with connected associated Coxeter graph. We exhibit a generating set of the centralizer of A X in A . Moreover, we prove that there exists X ′ ⊆ Σ such that A X ′ is conjugate to A X and such that the centralizer of A X ′ in A is generated by the centers of all the parabolic subgroups containing A X ′ .