in this paper, the urysohn and completely hausdorff axioms in general topology are generalized to l-topological spaces so as to be compatible with pointwise metrics. some properties and characterizations are also derived

We will extend the main result of [1] to non-unital case with a totally different proof. More precisely, we give an abstract characterization arbitrary self-adjoint weak⁎-closed subspace L(H) (equipped induced matrix norm, cone and weak⁎-topology). In order do this, analogue Bonsall for ⁎-operator spaces equipped closed cones.

we show that the category of convergence approach spaces is a simultaneously reective and coreective subcategory of the category of latticevalued limit spaces. further we study the preservation of diagonal conditions, which characterize approach spaces. it is shown that the category of preapproach spaces is a simultaneously reective and coreective subcategory of the category of lattice-valued p...

In a previous paper [6], the authors introduced the hyperbolic topology on a metric space, which is weaker than the metric topology and naturally derived from the Lawson topology on the space of formal balls. In this paper, we characterize spaces Lp(Ω,Σ, μ) on which the hyperbolic topology induced by the norm ∥·∥p coincides with the norm topology. We show the following. (1) The hyperbolic topol...

This work consists in a numerically evaluation of elastic fields distribution, caused by intrinsic dislocation networks placed at a nanometric trilayers interfaces, in order to estimate their influence on the surface topology during heterostructure operation. The organization of nanostructures is ensured by the knowledge of different elastic fields caused by buried dislocation networks and calc...

in this paper, we study some properties of the near sr-compactnessin l-topological spaces, where l is a fuzzy lattice. the near sr-compactness isa kind of compactness between lowen’s fuzzy compactness and sr-compactness,and it preserves desirable properties of compactness in general topologicalspaces.

Following the idea of $L$-fuzzy neighborhood system as introduced byFu-Gui Shi, and its generalization to $(L,M)$-fuzzy neighborhood system, the relationship between  $(L,M)$-fuzzy topology and $(L,M)$-fuzzy neighborhood system will be further studied. As an application of the obtained results, we will describe the initial structures of $(L,M)$-fuzzy neighborhood subspaces and $(L,M)$-fuzzy top...

Certain corrections are needed in this paper concerning the definition and properties of the weak topology on 12. Instead of characterising it in terms of converging sequences as on p. 7, one should define the weak topology as the coarsest topology for which the evaluations f --+ f o h(t)dr(t), f E ]2, are continuous for all continuous h(t) of compact support. With this topology, 12 is a Tihono...

In this paper, we introduce the concepts of L-fuzzy generalized neighborhood system(f-gns for short) and L-fuzzy generalized topology (fgt, for short)(where L is a fuzzy lattice) which are generalizations of generalized topology and neighborhood systems defined by Csaszar[5]. We also introduce and investigate with the help of these new concepts the concepts of L-(ψ1, ψ2) continuity and L-fuzzy ...

in this paper a particular case of z-ideals, called strongly z-ideal, is defined by introducing zero sets in pointfree topology. we study strongly z-ideals, their relation with z-ideals and the role of spatiality in this relation. for strongly z-ideals, we analyze prime ideals using the concept of zero sets. moreover, it is proven that the intersection of all zero sets of a prime ideal of c(l),...