in this paper, we have dened and studied a generalized form of topological vectorspaces called s-topological vector spaces. s-topological vector spaces are dened by using semi-open sets and semi-continuity in the sense of levine. along with other results, it is provedthat every s-topological vector space is generalized homogeneous space. every open subspaceof an s-topological vector space is ...

In this paper we find sufficient conditions on primitive inverse topological semigroup S under which: the inversion inv : (H(S)) (H(S)) is continuous; we show that every topologically periodic countable compact primitive inverse topological semigroups with closed H-classes is topologically isomorphic to an orthogonal sum P i2= Bi (Gi) of topological Brandt extensions Bi (Gi) of countably compac...

We have studied the average properties and the topological correlations of computer-simulated two-dimensional (2D) aggregating systems at different initial surface packing fractions. For this purpose, the centers of mass of the growing clusters have been used to build the Voronoi diagram, where each cell represents a single cluster. The number of sides (n) and the area (A) of the cells are rela...

Magnons and phonons are two fundamental neutral excitations of magnetically ordered materials which can significantly dominate the low-energy thermal properties. In this work we study interplay magnons in honeycomb Kagome lattices. When mirror reflection with respect to magnetic ordering direction is broken, symmetry-allowed in-plane Dzyaloshinskii-Moriya (DM) interaction will couple magnon-pol...

Symmetry breaking is ubiquitous in nature and represents the key mechanism behind rich diversity of patterns exhibited by nature. One commonly introduces an order parameter field to describe onset of qualitatively new ordering in a system on varying a relevant control parameter driving a symmetry breaking transition. In case of continuous symmetry breaking an order parameter consists of two qua...

In this paper, we define topological hyperrings and study their basic concepts which supported by illustrative examples. We show some differences between topological rings and topological hyperrings. Also, by the fundamental relation $\Gamma^{*}$, we indicate the role of complete parts (saturated subsets) and complete hyperrings in topological hyperrings and specially we show that if every (clo...

In this paper, we have dened and studied a generalized form of topological vector spaces called s-topological vector spaces. s-topological vector spaces are dened by using semi-open sets and semi-continuity in the sense of Levine. Along with other results, it is proved that every s-topological vector space is generalized homogeneous space. Every open subspace of an s-topological vector space is...

the notion of generalized locally bounded $i$-topological vectorspaces is introduced. some of their important properties arestudied. the relationship between this kind of spaces and thelocally bounded $i$-topological vector spaces introduced by wu andfang [boundedness and locally bounded fuzzy topological vectorspaces, fuzzy math. 5 (4) (1985) 87$-$94] is discussed. moreover, wealso use the fam...

Let U0, U1 be two normal measures on κ. We say that U0 is in the Mitchell ordering less than U1, U0 C U1, if U0 ∈ Ult(V,U1). The relation is well-known to be transitive and well-founded. It has been an open problem to find a model where C embeds the four-element poset . We find a generic extension where all well-founded posets are embeddable. Hence there is no structural restriction on the Mitc...