We study the first order form of the NS string sigma model allowing for worldsheet couplings corresponding on the target space to a bi-vector, a two-form and an inverse metric. Lifting the topological sector of this action to three dimensions produces several Wess-Zumino like terms which encode the bi-vector generalization of the Courant bracket. This bracket may be familiar to physicists throu...

I would like to thank the organizers of the UNISA Topology Workshop, Koena Rufus Nailana and Sergio Salbany, for doing an excellent job acquiring funding, making arrangements, and especially for assembling an enthusiastic group of participants. An ordered topological space (X, τ,≤) is a set X with a topology τ and a partial order ≤. We usually assume some forms of compatibility between the topo...

In this paper, by using a special family of filters $mathcal{F}$ on an EQ-algebra $E$, we construct a topology $mathcal{T}_{mathcal{mathcal{F}}}$ on $E$ and show that $(E,mathcal{T}_{mathcal{F}})$ is a topological EQ-algebra. First of all, we give some properties of topological EQ-algebras and investigate the interaction of topological EQ-algebras and quotient topological EQ-algebras. Then we o...

In this article we study two different generalizations of von Neumann regularity, namely strong topological regularity and weak regularity, in the Banach algebra context. We show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. Then we consider strong topological regularity of certain concrete algebras. Moreover we obtain ...

Example 2 (Convexity of a probability vector space) Show that the probability vector space is a convex set. Answer: Consider a random variable X with alphabet X = 1, ..., k. The probability vector space PX = [PX (1) , PX (2) , ..., PX (k)] ∈ R, is the set of all vectors for which PX (i) ≥ 0 ∀i ∈ X , and ∑K i=1 PX (i) = 1. Now consider two probability vectors P (1) X and P (2) X , and the vector

Our primary query is to Önd conditions under which the closure of a preorder on a topological space remains transitive. We study this problem for translation invariant preorders on topological groups. The results are fairly positive; we Önd that the closure of preorders and normal-orders remain as such in this context. The same is true for factor orders as well under quite general conditions. I...

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...

Example 2 (Convexity of a probability vector space) Show that the probability vector space is a convex set. Answer: Consider a random variable X with alphabet X = 1, ..., k. The probability vector space PX = [PX (1) , PX (2) , ..., PX (k)] ∈ R, is the set of all vectors for which PX (i) ≥ 0 ∀i ∈ X , and ∑K i=1 PX (i) = 1. Now consider two probability vectors P (1) X and P (2) X , and the vector

Example 2 (Convexity of a probability vector space) Show that the probability vector space is a convex set. Answer: Consider a random variable X with alphabet X = 1, ..., k. The probability vector space PX = [PX (1) , PX (2) , ..., PX (k)] ∈ R, is the set of all vectors for which PX (i) ≥ 0 ∀i ∈ X , and ∑K i=1 PX (i) = 1. Now consider two probability vectors P (1) X and P (2) X , and the vector