In a recent paper (Cf. [19]), we have presented the definitions and essential properties of generalized topological operators 
 g-Int_g, g-Cl_g : P (Ω) −→ (g-T_g-interior g-T_g-closure operators) in space T_g = (Ω, T_g) (T_g-space). Principally, have
 shown that (g-Int_g , g-Cl_g) × is ∅)-grounded, (expansive, non-expansive), (idempotent, idempotent) (∩, ∪)-additive. We also g-Int_g f...

The doubly connected polygonal geometry of planar graphene rings is found to bring forth topological configurations for accessing nontrivial relativistic quantum field (RQF) theory models that carry beyond the constant-mass Dirac-fermion theory. These include the generation of sign-alternating masses, solitonic excitations, and charge fractionization. The work integrates a RQF Lagrangian formul...

we show that the lattice of all ideals of a ring $r$ can be embedded in the lattice of all its fuzzyideals in uncountably many ways. for this purpose, we introduce the concept of the generalizedcharacteristic function $chi _{s}^{r} (a)$ of a subset $a$ of a ring $r$ forfixed $r , sin [0,1] $ and show that $a$ is an ideal of $r$ if, and only if, its generalizedcharacteristic function $chi _{s}^{...

In a generalized topological space Tg = (Ω, ) (Tg -space), various ordinary operators -operators), namely, int_g, cl_g, ext_g, fr_g, der_g, 
 cod_g : P (Ω) −→ (T_g-interior, T_g-closure, T_g-exterior, T_g-frontier, T_g-derived, T_g-coderived operators), are defined in terms of sets (T_g-sets). Accordingly, T_g-operators (g-T_g-operators), g-Int_g, g-Cl_g, g-Ext_g, g-Fr_g, g-Der_g, g-Cod_g ...

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.

Lattice actions and topological charges that are classically and quantum mechanically perfect (i.e. free of lattice artifacts) are constructed analytically for the quantum rotor. It is demonstrated that the Manton action is classically perfect while the Villain action is quantum perfect. The geometric construction for the topological charge is only perfect at the classical level. The quantum pe...

The fermionic topological charge of lattice gauge fields, given in terms of a spectral flow of the Hermitian Wilson–Dirac operator, or equivalently, as the index of Neuberger’s lattice Dirac operator, is shown to have analogous properties to Lüscher’s geometrical lattice topological charge. The main new result is that it reduces to the continuum topological charge in the classical continuum lim...

Electrons hopping on the sites of a three-dimensional pyrochlore lattice are shown to form topologically nontrivial insulating phases when the spin-orbit (SO) coupling and lattice distortions are present. Of 16 possible topological classes 9 are realized for various parameters in this model. Specifically, at half-filling an undistorted pyrochlore lattice with a SO term yields a "pristine" stron...

It is shown that when the underlying sigma model of bosonic string theory is written in terms of single-valued fields, which live in the covering space of the target space, Abelian T-duality survives lattice regularization of the world-sheet. The projection onto the target-space is implemented through a sum over cohomology, which bears resemblance to summing over topological sectors in Yang-Mil...

In this paper, the concepts of derived sets and derived operators are generalized to $(L, M)$-fuzzy topological spaces and their characterizations are given.What is more, it is shown that the category of stratified $(L, M)$-fuzzy topological spaces,the category of stratified $(L, M)$-fuzzy closure spaces and the category of stratified $(L, M)$-fuzzy quasi-neighborhood spaces are all isomorphic ...