‎‎The purpose of this paper is to introduce new methods for constructing generalized groups, generalized topological groups and top spaces. We study some properties of these structures and present some relative concrete examples. Moreover, we obtain generalized groups by using of Hilbert spaces and tangent spaces of Lie groups, separately.

We show that the solid hull of every weakly precompact set a Banach lattice E is if and only order interval in precompact, or equivalently, disjoint compact precompact. Some results on domination property for positive operators are obtained. Among other things, we that, pair lattices F with $$\sigma $$ -Dedekind complete, operator from to dominated by either norm $$E^{\prime }$$ continuous else

Let X be a completely regular Hausdorff space, E a Hausdorff topological vector space, CL(E) the algebra of continuous operators on E, V a Nachbin family on X and F ⊆ CVb(X,E) a topological vector space (for a given topology). If π : X → CL(E) is a mapping, consider the induced multiplication operator Mπ : F → F given by Mπ(f)(x) := π(x)f(x), f ∈ G, x ∈ coz(F). In this paper we give necessary a...

In this paper, the notion of generalized regular fuzzy irresolute, generalized regular fuzzy irresolute open  and generalized regular fuzzy irresolute closed maps in fuzzy  topological spaces are introduced and studied. Moreover, some separation axioms and $r$-GRF-separated sets are established. Also, the relations between generalized regular fuzzy continuous maps and generalized regular fuzzy ...

in this paper, the urysohn and completely hausdorff axioms in general topology are generalized to l-topological spaces so as to be compatible with pointwise metrics. some properties and characterizations are also derived

The paper is an attempt to represent a study of limit points, boundary points, exterior points, border, interior points and closure points in the common generalized topological space. This paper takes a look at the possibilities of an extended topological space and it also considers the new characterizations of dense set.

In dealing with transformation group, topological approach is very natural. But, it is not sufficient to investigate geometric properties of transformation group and we need geometric method. Frankel-McDuff Conjecture is very interesting in the point that it shows struggling between topological method and geometric method. In this paper, the author suggest generalized FrankelMcDuff conjecture a...

Given a nilpotent orbit O of a real, reductive algebraic group, a necessary condition is given for the existence of a tempered representation π such that O occurs in the wave front cycle of π. The coefficients of the wave front cycle of a tempered representation are expressed in terms of volumes of precompact submanifolds of an affine space.

Using the Generalized Differential Calculus, we establish the generalized Chern-Weil homomormism, re-derive the geometric properties for both P (M4, G) and pseudo-Riemannian spacetime manifolds from BF theories, and obtain the generalized Chern-Simons term for BF theory in four dimensions. It gives a direct relation between these two types of topological field theories. We then obtain the BF gr...