in this paper, a certain new connectedness of l-fuzzy subsets inl-topological spaces is introduced and studied by means of preclosed sets. itpreserves some fundamental properties of connected set in general topology.especially the famous k. fan’s theorem holds.

We propose a general construction of commuting projector lattice models for 2D and 3D topological phases enriched by U(1) symmetry, with finite-dimensional Hilbert space per site. The starts from model the phase decorates charges to state in consistent manner. show that all symmetry-enriched phases, which allow gapped boundaries without breaking can be realized through our construction. also co...

We propose a fully immersed topology optimization procedure to design structures with tailored fracture resistance under linear elastic mechanics assumptions for brittle materials. use level set function discretized by radial basis functions represent the and Interface-enriched Generalized Finite Element Method (IGFEM) obtain an accurate structural response. The technique assumes that cracks ca...

The notion of stratified (L, M)-semiuniform convergence tower spaces is introduced, which extends the notions ofprobabilistic semiuniform convergence spaces and lattice-valued semiuniform convergence spaces. The resulting categoryis shown to be a strong topological universe. Besides, the relations between our category and that of stratified (L, M)-filter tower spaces are studied.

In this paper, a new definition of locally convex L-topological vector spaces is given. The relationship between this new definition and the previous definition of locally convex L-topological vector spaces given by Yan and Fang in 1999 is investigated. Moreover, the concept of generalized L-fuzzy semi-norm is introduced. By using a family of generalized L-fuzzy semi-norms, a characterization o...

Department of Mathematics, Faculty of Science, El-Mansoura University, El-Mansoura, Egypt Abstract: In this research work, new topological notions are proposed and investigated. The notions are named final characterized L-spaces and initial and final characterized L-topological groups. The properties of such notions are deeply studied. We show that all the final lefts and all the final characte...