In this paper, it is shown that the category of stratified $L$-generalized convergence spaces is monoidal closed if the underlying truth-value table $L$ is a complete residuated lattice. In particular, if the underlying truth-value table $L$ is a complete Heyting Algebra, the Cartesian closedness of the category is recaptured by our result.

The projective tensor product in a category of topologicalR-modules (where R is a topological ring) can be defined in Top, the category of topological spaces, by the same universal property used to define the tensor product of R-modules in Set. In this article, we extend this definition to an arbitrary topological category X and study how the cartesian closedness of X is related to the monoidal...

Lattice-valued semiuniform convergence structures are important mathematical in the theory of lattice-valued topology. Choosing a complete residuated lattice $L$ as background, we introduce new type filters using tensor and implication operations on $L$, which is called $\top$-filters. By means $\top$-filters, propose concept $\top$-semiuniform counterpart structures. Different from usual discu...

We demonstrate how the identity N N = N in a monoidal category allows us to construct a functor from the full subcategory generated by N and to the endomorphism monoid of the object N. This provides a categorical foundation for one-object analogues of the symmetric monoidal categories used by J.-Y. Girard in his Geometry of Interaction series of papers, and explicitly described in terms of inve...

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...

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...