in the present paper, we introduce some new sequence spaces derived by riesz mean and the notions of almost and strongly almost convergence in a real 2-normed space. some topological properties of these spaces are investigated. further, new concepts of statistical convergence which will be called weighted almost statistical convergence, almost statistical convergence and statistical convergence...

We describe algebraic obstruction theories for realizing an abstract (co)algebra K∗ over the mod p Steenrod algebra as the (co)homology of a topological space, and for distinguishing between the p-homotopy types of different realizations. The theories are expressed in terms of the Quillen cohomology of K∗.

in this paper, we establish the theory of fuzzy ideal convergence on completely distributive lattices and give characterizations of some topological notions. we also study fuzzy limit structures and discuss the relationship between fuzzy co-topologies and fuzzy limit structures.

The aim of this paper is to study L-fuzzy uniformizable spaces. A new kind of topological fuzzy remote neighborhood system is defined and used for investigating the relationship between L-fuzzy co-topology and L-fuzzy (quasi-)uniformity. It is showed that this fuzzy remote neighborhood system is different from that in [23] when U is an Lfuzzy quasi-uniformity and they will be coincident when U ...

This paper generalizes the notion of a toric variety. In particular, these generalized toric varieties include examples of non-normal non-quasiprojective toric varieties. Such an example seems not to have been noted before in the literature. This generalization is achieved by replacing a fan of strictly rational polyhedral cones in a lattice with a monoided space, that is a topological space eq...

We lay out an experiment to realize time-reversal invariant topological insulators in alkali atomic gases. We introduce an original method to synthesize a gauge field in the near field of an atom chip, which effectively mimics the effects of spin-orbit coupling and produces quantum spin-Hall states. We also propose a feasible scheme to engineer sharp boundaries where the hallmark edge states ar...

let $g$ be a graph and let $m_{ij}(g)$, $i,jge 1$, be the number of edges $uv$ of $g$ such that ${d_v(g), d_u(g)} = {i,j}$. the {em $m$-polynomial} of $g$ is introduced with $displaystyle{m(g;x,y) = sum_{ile j} m_{ij}(g)x^iy^j}$. it is shown that degree-based topological indices can be routinely computed from the polynomial, thus reducing the problem of their determination in each particular ca...

Abstract. The semi-topological K-theory K ∗ (X) of a quasi-projective complex algebraic variety X is based on the notion of algebraic vector bundles modulo algebraic equivalence. This theory is given as the homotopy groups of an infinite loop space K(X) which is equipped with maps K(X) → K(X), K(X) → Ktop(Xan) whose composition is the natural map from the algebraic K-theory of X to the topologi...

We investigate under what conditions a co-recursively enumerable set S in a computable metric space (X, d, α) is recursive. The topological properties of S play an important role in view of this task. We first study some properties of computable metric spaces such as the effective covering property. Then we examine co-r.e. sets with disconnected complement, and finally we focus on study of chai...