Displaying similar documents to “When ( E , σ ( E , E ' ) ) is a D F -space?”

Some characterization of locally nonconical convex sets

Witold Seredyński (2004)

Czechoslovak Mathematical Journal

Similarity:

A closed convex set Q in a local convex topological Hausdorff spaces X is called locally nonconical (LNC) if for every x , y ∈ Q there exists an open neighbourhood U of x such that ( U ∩ Q ) + 1 2 ( y - x ) ⊂ Q . A set Q is local cylindric (LC) if for x , y ∈ Q , x ≠ y , z ∈ ( x , y ) there exists an open neighbourhood U of z such that U ∩ Q (equivalently: b d ( Q ) ∩ U ) is a union of open segments parallel to [ x , y ] . In this paper we prove that these two notions are equivalent. The properties LNC and LC were investigated in [3], where the implication L N C ⇒ L C was proved in...

Distributivity of strong implications over conjunctive and disjunctive uninorms

Daniel Ruiz-Aguilera, Joan Torrens (2006)

Kybernetika

Similarity:

This paper deals with implications defined from disjunctive uninorms U by the expression I ( x , y ) = U ( N ( x ) , y ) where N is a strong negation. The main goal is to solve the functional equation derived from the distributivity condition of these implications over conjunctive and disjunctive uninorms. Special cases are considered when the conjunctive and disjunctive uninorm are a t -norm or a t -conorm respectively. The obtained results show a lot of new solutions generalyzing those obtained in previous works...

On the structure of continuous uninorms

Paweł Drygaś (2007)

Kybernetika

Similarity:

Uninorms were introduced by Yager and Rybalov [13] as a generalization of triangular norms and conorms. We ask about properties of increasing, associative, continuous binary operation U in the unit interval with the neutral element e ∈ [ 0 , 1 ] . If operation U is continuous, then e = 0 or e = 1 . So, we consider operations which are continuous in the open unit square. As a result every associative, increasing binary operation with the neutral element e ∈ ( 0 , 1 ) , which is continuous in the open unit square may be...