In object-oriented systems, object associations generally result in a complex structure whose precise description is a crucial part of the sys-tem's formal speciication. A particularly common object association arises when one object exclusively controls (owns) another. As exclusive object control is an important aspect of safety and security critical systems, speciic notation to capture direct...

Assuming that this is false, one can choose a subsequence, denoted by u j again, such that ‖u j‖ > j . Let z j := u j/‖u j‖. Then ‖z j‖ = 1, z j is orthogonal to N (I + T ), and z j + T z j = f j/‖u j‖ → 0. As before, it follows that z j → z in H , and passing to the limit in the equation for z j one gets z + T z = 0. Since z is orthogonal to N (I + T ), it follows that z = 0. This is a contrad...

Open problems and recent results on causal completeness of probabilistic theories – p. 1/2 Structure Informal motivation of the problem of causal closedness: Reichenbach's Common Cause Principle Causal closedness of classical probability spaces (notion + propositions) Causal closedness – quantum probability spaces (notion + proposition) Spacelike correlations predicted by quantum field theory L...

This paper investigates dynamic semantics of conversations from the point of view of semantical closedness, presuppositions and shared belief/common knowledge updates, by analyzing the meta-expression “what do you mean (by X)?” into three major usages: semantic repair initiation, intentional repair initiation, and inferential repair initiation, since these three usages are deeply related with t...

Compactness and closedness are some of the important properties for studying topological spaces. Several types of these concepts (semi-compactness, pre-compactness, β-compactness,. . ., S-closedness, H-closedness, etc) occur in the literature. In this paper, we applied concept of φ operation which defined by Csaszar [8] to unify and generalized several characterizations and properties of lots o...

The purpose of this paper is to introduce the concept of pairwise F-closedness in bitopological spaces. This space contains both of pairwise strongcompactness and pairwise S-closedness and contained in pairwise quasi H-closedness. The characteristics and relationships concerning this new class of spaces with other corresponding types are established. Moreover, several of its basic and important...

Let X be a topological space and let Φ ⊂ C(X). Then there exists a topological space Y containing X as a subspace and such that Φ = C(Y )|X, if and only if Φ is weakly composition closed, i.e., for any index set I, any fi ∈ Φ (i ∈ I) and any continuous map k : R → R we have k ◦ 〈fi〉 ∈ Φ, where 〈fi〉 : X → R is the map with i-th coordinate fi. The analogous statement is valid for functions to any...

This paper investigates relations between team learning and a quasi-closedness property inherent in many identiication types considered in inductive inference. This property is as follows: there exists such n that, if every union of n ?1 classes out of U1; : : : ; Un is identiiable, so is the union of all n classes. This property can be formulated in terms of team learning, but in practice the ...

the purpose of this paper is to introduce the concept of pairwise f-closedness in bitopological spaces. this space contains both of pairwise strongcompactness and pairwise s-closedness and contained in pairwise quasi h-closedness. the characteristics and relationships concerning this new class ofspaces with other corresponding types are established. moreover, several ofits basic and important p...

Obtaining a weaker condition that preserves some inspired topological properties is always desirable. As result, we introduce the concept of infra-fuzzy topology, which subset family degrades fuzzy topology by omitting closedness under arbitrary unions. Fundamental spaces are investigated, including open and closed sets, interior closure operators, boundary set. It not possible to expect latter...