I discuss several novel topological phases in correlated electron systems, realized through spin-orbit interactions and lattice effects especially narrow-band systems. The first realizes the fractional quantum Hall effect using geometric frustration and ferromagnetism to obtain a nearly flat band with a large bandgap and non-zero Chern number. This system can support this effect at high tempera...

We show that the lattice of compactifications of a topological group $G$ is a complete lattice which is isomorphic to the lattice of all closed normal subgroups of the Bohr compactification $bG$ of $G$. The correspondence defines a contravariant functor from the category of topological groups to the category of complete lattices. Some properties of the compactification lattice of a topological ...

Abstract The fundamental properties for the spin and orbital angular momentum are analyzed using acoustic evanescent Bessel beams. calculations reveal that transversal spin, canonical momentum, proportional to ratio l /ω where is topological charge ω frequency. This analysis shows complex Poynting vector density exhibits interesting features related electromagnetic case.

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...

For a nonempty compact set Ω ⊆ R we determine the maximal possible dimension of a subspace X ⊆ Pm(Ω) of polynomial functions over Ω with degree at most m which possesses a positive basis. The exact value of this maximum depends on topological features of Ω, and we will see that in many of the cases m can be achieved. Whereas only for low m or finite sets Ω is it possible that we have a subspace...

In this paper, the denition of net-theoretical L-generalized convergencespaces is proposed. It is shown that, for L a frame, the category ofenriched L-fuzzy topological spaces can be embedded in that of L-generalizedconvergence spaces as a reective subcategory and the latter is a cartesianclosedtopological category.

Let G be a simple connected graph and {v_1,v_2,..., v_k} be the set of pendent (vertices of degree one) vertices of G. The reduced distance matrix of G is a square matrix whose (i,j)-entry is the topological distance between v_i and v_j of G. In this paper, we compute the spectrum of the reduced distance matrix of the generalized Bethe trees.

Rough set theory is a powerful mathematical tool for dealing with inexact, uncertain or vague information. The core concept of rough set theory are information systems and approximation operators of approximation spaces. In this paper, we study the relationships between mset relations and mset topology. Moreover, this paper concerns generalized mset approximation spaces via topological methods ...

Topological entropy is one of the most difficult entropies to be used to analyze the DNA sequences, due to the finite sample and high-dimensionality problems. In order to overcome these problems, a generalized topological entropy is introduced. The relationship between the topological entropy and the generalized topological entropy is compared, which shows the topological entropy is a special c...