Purpose: In this paper, we extend the concept of covering DIMENSION of general TOPOLOGICAL spaces to L-TOPOLOGICAL spaces using a-Q-covers and quasi-coincidence relation.Methods: DIMENSION theory is a branch of topology devoted to the definition and study of the notion of DIMENSION in certain classes of TOPOLOGICAL spaces. The DIMENSION of a general TOPOLOGICAL space X can be defined in three different ways: the small inductive DIMENSION indX, the large inductive DIMENSION IndX, and the covering DIMENSION dimX. The covering DIMENSION dim behaves somewhat better than the other two DIMENSIONs, i.e., that for the DIMENSION dim, a large number of theorems of the classical theory can be extended to general TOPOLOGICAL spaces. Also, there is a substantial theory of covering DIMENSION for normal spaces.Results: A characterization of covering DIMENSION in the weakly induced L-TOPOLOGICAL spaces is obtained. Moreover, a characterization of covering DIMENSION for fuzzy normal spaces is also obtained.Conclusions: Finally, This paper provides some brief sketches regarding the topics covering DIMENSION in L-TOPOLOGICAL spaces and covering DIMENSION for fuzzy normal spaces. The neighborhood structure used for the investigations is the quasi-coincident neighborhood structure.

Introduction: Graph theoretical analysis of functional Magnetic Resonance Imaging (fMRI) data has provided new measures of mapping human brain in vivo. Of all methods to measure the functional connectivity between regions, Linear Correlation (LC) calculation of activity time series of the brain regions as a linear measure is considered the most ubiquitous one. The strength of the dependence obligatory for graph construction and analysis is consistently underestimated by LC, because not all the bivariate distributions, but only the marginals are Gaussian. In a number of studies, Mutual Information (MI) has been employed, as a similarity measure between each two time series of the brain regions, a pure nonlinear measure. Owing to the complex fractal organization of the brain indicating self-similarity, more information on the brain can be revealed by fMRI Fractal DIMENSION (FD) analysis.Methods: In the present paper, Box-Counting Fractal DIMENSION (BCFD) is introduced for graph theoretical analysis of fMRI data in 17 methamphetamine drug users and 18 normal controls.Then, BCFD performance was evaluated compared to those of LC and MI methods. Moreover, the global TOPOLOGICAL graph properties of the brain networks inclusive of global efficiency, clustering coefficient and characteristic path length in addict subjects were investigated too.Results: Compared to normal subjects by using statistical tests (P<0.05), TOPOLOGICAL graph properties were postulated to be disrupted significantly during the resting-state fMRI.Conclusion: Based on the results, analyzing the graph TOPOLOGICAL properties (representing the brain networks) based on BCFD is a more reliable method than LC and MI.

In this paper we give some characterizations of TOPOLOGICAL extreme amenability. Also we answer a question raised by Ling [5]. In particular we prove that if T is a Borel subset of a locally compact semigroup S such that M(S)* has a multiplicative TOPOLOGICAL left invariant mean then T is TOPOLOGICAL left lumpy if and only if there is a multiplicative TOPOLOGICAL left invariant mean M on M(S)* such that M(XT)=1, where XT is the characteristic functional of T. Consequently if T is a TOPOLOGICAL left lumpy locally compact Borel subsemigroup of a locally compact semigroup S, then T is extremely TOPOLOGICAL left amenable if and only if S is.

In this paper, we study the separtion axioms T 0, T 1, T 2 and T 5/2 on TOPOLOGICAL and semiTOPOLOGICAL residuated lattices and we show that they are equivalent on TOPOLOGICAL residuated lattices. Then we prove that for every infinite cardinal number a, there exists at least one nontrivial Hausdor TOPOLOGICAL residuated lattice of cardinality a. In the follows, we obtain some conditions on (semi) TOPOLOGICAL residuated lattices under which this spaces will convert into regular and normal spaces.Finally by using of regularity and normality, we convert (semi) TOPOLOGICAL residuated lattices into metrizable TOPOLOGICAL residuated lattices.

In this paper we introduce the concept of TOPOLOGICAL number for locally convex TOPOLOGICAL spaces and prove some of its properties. It gives some criterions to study locally convex TOPOLOGICAL spaces in a discrete approach.

In addition to exploring constructions and properties of limits and colimits in categories of TOPOLOGICAL algebras, we study special subcategories of TOPOLOGICAL algebras and their properties. In particular, under certain conditions, reflective subcategories when paired with TOPOLOGICAL structures give rise to reflective subcategories and epireflective subcategories give rise to epireflective subcategories.

Hyperdiamonds are covalently bonded fullerenes in crystalline forms, more or less related to diamond, and having a significant amount of sp3 carbon atoms. Design of several hypothetical crystal networks was performed by using our original software programs CVNET and NANO-STUDIO. The topology of the networks is described in terms of the net parameters and several counting polynomials, calculated by NANO-STUDIO, OMEGA and PI software programs.

In this paper, we have defined and studied a generalized form of TOPOLOGICAL vector spaces called s-TOPOLOGICAL vector spaces. s-TOPOLOGICAL vector spaces are defined by using semi-open sets and semi-continuity in the sense of Levine. Along with other results, it is proved that every s-TOPOLOGICAL vector space is generalized homogeneous space. Every open subspace of an s-TOPOLOGICAL vector space is an s-TOPOLOGICAL vector space. A homomorphism between s-TOPOLOGICAL vector spaces is semi-continuous if it is s-continuous at the identity.

The main purpose of this paper is to introduce a concept of L- fuzzifying TOPOLOGICAL groups (here L is a completely distributive lattice) and discuss some of their basic properties and the structures. We prove that its corresponding L-fuzzifying neighborhood structure is translation invariant. A characterization of such TOPOLOGICAL groups in terms of the corresponding L- fuzzifying neighborhood structure of the unit is given. It is shown that the category of L-fuzzifying TOPOLOGICAL groups L-FYTPG is TOPOLOGICAL over the category of groups GRP with respect to the forgetful functor. As an application, the conclusion that the product of L-fuzzifying TOPOLOGICAL groups is also an L-fuzzifying TOPOLOGICAL group is proved. Finally, it is proved the forgetful functor preserves the product.