In this note we propose a new way of constructing compact 7-manifolds with a closed G 2-structure. As a result we find a first example of a closed G 2-structure on S 3 × S 4. We also prove that any integral closed G 2-structure on a compact 7-manifold M 7 can be obtained by embedding M 7 to a universal space (W 3(80+8.C 3 8) , h). MSC: 53C10, 53C42 Key words: closed G 2-structures, submanifolds...

In this paper we have introduced a new class of closed in topological spaces called g**-closed sets and study some its properties . Further introduce the concept g**-continuous functions , g**-irresolute As an application two news paces namely T **-space, **T - space .Further, g**-continuous, mappings are also investigated

let $mathbb{f}$ be an algebraically closed field of prime characteristic $p>2$ and $(g, [p])$ a finite-dimensional restricted lie superalgebra over $mathbb{f}$. it is showed that anyfinite-dimensional indecomposable $g$-module is a module for a finite-dimensional quotient of the universal enveloping superalgebra of $g$. these quotient superalgebras are called the generalized reduced enveloping ...

a watching system in a graph $g=(v, e)$ is a set $w={omega_{1}, omega_{2}, cdots, omega_{k}}$, where $omega_{i}=(v_{i}, z_{i}), v_{i}in v$ and $z_{i}$ is a subset of closed neighborhood of $v_{i}$ such that the sets $l_{w}(v)={omega_{i}: vin omega_{i}}$ are non-empty and distinct, for any $vin v$. in this paper, we study the watching systems of line graph $k_{n}$ which is called triangular grap...

The class of ω-closed subsets of a space (X ,τ) was defined to introduce ω-closed functions. The aim of this paper is to introduce and study the class of gω-closed sets. This class of sets is finer than g-closed sets and ω-closed sets. We study the fundamental properties of this class of sets. In the space (X ,τω), the concepts closed set, g-closed set, and gω-closed set coincide. Further, we i...

Let G be a connected simple graph. We prove that G is a closed graph if and only if G is a proper interval graph. As a consequence we obtain that there exist linear-time algorithms for closed graph recognition.

Let G be a linear algebraic group, H a closed subgroup of G and X a G-variety. This paper explores the connection between G-orbits and H-orbits in X, concentrating in particular on the question of when we have the implications G · x closed in X implies H · x closed in X, and vice versa. Some of the general results found in this paper are then used in the special case where G and H are reductive...

Let G be a nonempty closed (resp. bounded closed) subset in a strongly convex Banach space X. Let BðXÞ denote the space of all nonempty bounded closed subsets of X endowed with the Hausdorff distance and let BGðXÞ denote the closure of the set fA 2 BðXÞ : A \ G 1⁄4 ;g. We prove that E(G) (resp. Eo(G)), the set of all A 2 BGðXÞ (resp. A 2 BðXÞ) such that the minimization (resp. maximization) pro...

Let G be a non-trivial algebraically closed group and X be a subset of G generating G in infinitely many steps. We give a construction of a binary tree associated with (G,X). Using this we show that if G is ω1-existentially closed then it is strongly bounded.