the main purpose of this paper is to introduce a concept of$l$-fuzzifying topological groups (here $l$ is a completelydistributive lattice) and discuss some of their basic properties andthe structures. we prove that its corresponding $l$-fuzzifyingneighborhood structure is translation invariant. a characterizationof such topological groups in terms of the corresponding$l$-fuzzifying neighborhoo...

In this paper, the Urysohn, completely Hausdorff and completely regular axioms in $L$-topological spaces are generalized to $L$-fuzzy topological spaces. Each $L$-fuzzy topological space can be regarded to be Urysohn, completely Hausdorff and completely regular tosome degree. Some properties of them are investigated. The relations among them and $T_2$ in $L$-fuzzy topological spaces are discussed.

The role of generalized Bowen-Franks groups (BF-groups) as topological conjugacy invariants for T automorphisms is studied. Using algebraic number theory, a link is established between equality of BFgroups for different automorphisms (BF -equivalence) and an identical position in a finite lattice (L-equivalence). Important cases of equivalence of the two conditions are proved. Finally, a topolo...

A comparative study of 36 molecular descriptors derived from the topological distance matrix and van der Waals space is carried out within this paper. They are partitioned into 16 generalized topological distance matrix indices, 11 topological distance indices known in the literature (seven obtained from eigenvalues/eigenvectors of distance matrix), and 9 van der Waals molecular descriptors. Th...

We propose the lattice version of BF gravity action whose partition function leads to the product of a particular form of 15-j symbol which corresponds to a 4-simplex. The action is explicitly constructed by lattice B field defined on triangles and link variables defined on dual links and is shown to be invariant under lattice local Lorentz transformation and Kalb-Ramond gauge transformation. W...

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...

The generalized Mycielskians are the generalization of the Mycielski graphs, which were introduced by Mycielski in 1955. A topological index is a numeric parameter mathematically derived from a graph and is invariant under automorphism of graphs. Topological indices are widely used for establishing correlations between the structure of a molecular compound and its different physico-chemical pro...

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We study a class of lattice field theories in two dimensions that includes gauge theories. Given a two dimensional orientable surface of genus g, the partition function Z is defined for a triangulation consisting of n triangles of area ǫ. The reason these models are called quasi-topological is that Z depends on g, n and ǫ but not on the details of the triangulation. They are also soluble in the...