Abstract. A topological group H is called ω -narrow if for every neighbourhood V of it’s identity element there exists a countable set A such that V A = H = AV. A semigroup G is called a generalized group if for any x ∈ G there exists a unique element e(x) ∈ G such that xe(x) = e(x)x = x and for every x ∈ G there exists x − 1 ∈ G such that x − 1x = xx − 1 = e(x). Also le...

this paper deals with continuous frames and continuous riesz bases. we introduce continuous riesz bases and give some equivalent conditions for a continuous frame to be a continuous riesz basis. it is certainly possible for a continuous frame to have only one dual. such a continuous frame is called a riesz-type frame [13]. we show that a continuous frame is riesz-type if and only if it is a con...

We prove that in the weak topology of measure preserving transformations , a dense G has purely singular continuous spectrum in the orthocomplement of the constant functions. In the uniform topology, a dense G of aperiodic transformations has singular continuous spectrum. We show that a dense G of shift-invariant measures has purely singular continuous spectrum. These results stay true for Z d ...

Let G be a locally compact Abelian group; I’ the dual group of G; CO(l_’)the algebra of continuous functions on r which vanish at infinity; CB(17)the continuous, bounded functions on r; M(G) the algebra of bounded Borel measures on G; Ll(G) the algebra of absolutely continuous measures; and M(G)A the algebra of l?ourier-Stielt jes transforms. Let E denote a compact subset of I’, and let A(E) be...

It is a well known fact that we can deduce G continuous isophotes from a G continuous surface This paper gives answer to the reverse problem we deduce a G continuous surface from G continu ous isophotes on the surface We show how many families of isophotes we have to consider and what constraints apply Furthermore we apply the geodesic curvature and the thickness of isophotes as a surface inter...

Let G = (V (G), E(G)) be a multigraph. The degree of a vertex x in G is denoted by d(x), the greatest degree of a vertex – by ∆(G), the chromatic index of G – by χ ′ (G). Let R ⊆ V (G). An interval (respectively, continuous) on R t-coloring of a multigraph G is a proper coloring of edges of G with the colors 1, 2,. .. , t, in which each color is used at least for one edge, and the edges inciden...

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