The aim of this paper is to introduce a further generalization of compactness in generalized topological spaces. We define and study the concept of Dμ-compact spaces in generalized topological spaces. A space(X, μ) is Dμ-compact if every Dμ-cover of X has a finite Dμ-sub cover. Basic properties and characterizations of Dμ-compact space are established. Dμ-compactness in subspaces, products of g...

A.Pushpalatha et al [11] introduced the concept of τ-g-closed set in topological spaces. S.Eswaran and A.Pushpalatha [6] introduced and studied the properties of τ-generalized continuous maps and τ-gc-irresolute maps in topological spaces. In this paper, we introduce and study a new class of maps called τ-generalized open maps and the notion of τ-generalized homeomorphism and τ-gchomeomorphism ...

V. P. Zahariuta, in 1973, used the theory of Fredholm operators to develop a method to classify Cartesian products of locally convex spaces. In this work we modify his method to study the isomorphic classification of Cartesian products of the kind E0…a† E1 …b† where 1 % p;q < 1 , p ˆj q, a ˆ …an† nˆ1 and b ˆ …bn† nˆ1 are sequences of positive numbers and E0…a†, E1 …b† are respectively `p-finite...

Several specific types of generalized sets (briefly, g-T_g-sets in topological spaces T_g-spaces have been defined and investigated for various purposes from time to the literature T_g-spaces. Our recent research field a new class is reported herein as starting point more classes. It shown that superclass those whose elements are called open, closed, semi-open, semi-closed, pre-open, pre-closed...

A topological space $X$ is defined to have a neighborhood $P$-base at any $x\in X$ from some partially ordered set (poset) $P$ if there exists base $(U_p[x])_{p\in P}$ $x$ such that $U_p[x]\subseteq U_{p’}[x]$ for all $p\geq p’$ in $P$. We prove compact countable, hence metrizable, it has countable scattered height and $\mathcal {K}(M)$-base separable metric $M$. Banakh [Dissertationes Math...

in this paper we introduce a new definition of the first non-abelian cohomology of topological groups.  we relate the cohomology of a normal subgroup $n$ of a topological group $g$ and the quotient $g/n$ to the cohomology of $g$. we get the inflation-restriction exact sequence. also, we obtain a seven-term exact cohomology sequence up to dimension 2. we give an interpretation of the first non-a...

The massive sulfide deposits (VMS) from Mănăilă are associated with the metamorphic formations of Tulgheș Lithogroup Bucovinian Nappes Crystalline-Mesozoic Zone in Eastern Carpathians, Romania. following types ore were identified: pyrite-polymetallic, pyrite copper, compact and precompact quartz-precompact copper. polymetallic mineralization consists pyrite, chalcopyrite, sphalerite, galena, su...

In this paper we further study links between concentration of measure in topological transformation groups, existence of fixed points, and Ramsey-type theorems for metric spaces. We prove that whenever the group Iso (U) of isometries of Urysohn’s universal complete separable metric space U, equipped with the compact-open topology, acts upon an arbitrary compact space, it has a fixed point. The ...