With L a complete lattice and M a continuous lattice, this paper demonstrates an adjunction between M-valued L-topological spaces (i.e. (L,M)-topological spaces) and Idl(M)-valued L-topological spaces where Idl(M) is the complete lattice of all ideals of M. It is shown that the right adjoint functor provides a procedure of generating (L,M)-topologies from antitone families of (L,M)-topologies. ...

Non-standard overview on the possible formulation towards a unified model on the lattice is presented. It is based on the generalized gauge theory which is formulated by differential forms and thus expected to fit in a simplicial manifold. We first review suggestive known results towards this direction. As a small step of concrete realization of the program, we propose a lattice Chern-Simons gr...

Graphene sheets are combined of Honeycombs lattice carbon-carbon bonds which have high natural frequencies, high strength, and high conductivity. Due to important applications of the graphene sheets particularly at higher frequencies, the study of their dynamic behavior is important in this frequency range. From Molecular Dynamics (MD) point of view as the dimensions of graphene sheet incline, ...

We predict theoretical existence of intrinsic two-dimensional organic topological insulator (OTI) states in Cu-dicyanoanthracene (DCA) lattice, a system that has also been grown experimentally on Cu substrate, based on first-principle density functional theory calculations. The pz-orbital Kagome bands having a Dirac point lying exactly at the Fermi level are found in the freestanding Cu-DCA lat...

In this paper, we introduce and characterize the concept of fuzzy almost generalized $e$-continuous mappings. Several interesting properties of these mappings are also given. Examples and counter examples are also given to illustrate the concepts introduced in the paper. We also introduce the concept of fuzzy $f T_{frac{1}{2}}e$-space, fuzzy $ge$-space, fuzzy regular $ge$-space and  fuzzy gener...

Some necessary and sufficient conditions allowing a previously unknown space to be explored through scanning operators are reexamined with respect to measure theory. Some generalized conceptions of distances and dimensionality evaluation are proposed, together with their conditions of validity and range of application to topological spaces. The existence of a Boolean lattice with fractal proper...

Kondo insulators are a particularly simple type of heavy electron material, where a filled band of heavy quasiparticles gives rise to a narrow band insulator. Starting with the Anderson lattice Hamiltonian, we develop a topological classification of emergent band structures for Kondo insulators and show that these materials may host three-dimensional topological insulating phases. We propose a ...

Some necessary and sufficient conditions allowing a previously unknown space to be explored through scanning operators are reexamined with respect to measure theory. Some generalized conceptions of distances and dimensionality evaluation are proposed, together with their conditions of validity and range of application to topological spaces. The existence of a Boolean lattice with fractal proper...

We analyze topological objects in pure gluonic SU(2) lattice gauge theory and compute correlation functions between instantons and monopoles. Concerning the instantons we use geometric and field theoretic definitions of the topological charge. On a 12 × 4 lattice it turns out that topological quantities have a non-trivial local correlation. The auto-correlation functions of the topological char...

In this work we study the surface properties of topological systems, with a special focus on topological superconductors without inversion symmetry. These materials provide a rich playground for multiple topological phenomena, showing boundary modes with linear and (or) flat dispersion arising from complex nodal structures. A remarkable characteristic of topological phases is their robustness t...