In the past few years, research on sober spaces and well-filtered has got some breakthrough progress. this paper, we shall present a brief summarizing survey of such development. Furthermore, pose illustrate open problems spaces.

In this note we introduce a notion of essentially-Euclidean normed spaces (and convex bodies). Roughly speaking, an n-dimensional space is λ-essentially-Euclidean (with 0 < λ < 1) if it has a [λn]dimensional subspace which has further proportionally dimensional Euclidean subspaces of any proportion. We consider a space X1 = (Rn, ‖ · ‖1) with the property that if a space X2 = (Rn, ‖ · ‖2) is “no...

In this paper, we introduce and study the concept of $r$-fuzzy regular semi open (closed) sets in smooth topological spaces. By using $r$-fuzzy regular semi open (closed) sets, we define a new fuzzy closure operator namely $r$-fuzzy regular semi interior (closure) operator. Also, we introduce fuzzy regular semi continuous and fuzzy regular semi irresolute mappings. Moreover, we investigate the ...

In this paper, using pre-semi-open L-sets and their inequality, a new notion of PS-compactness is introduced in L-topological spaces, where L is a complete De Morgan algebra. This notion does not depend on the structure of the basis lattice L and L does not need any distributivity.

the aim of this paper is to show the importance of analytic hyperbolic geometry introduced in [9]. in [1], ungar and chen showed that the algebra of the group sl(2,c) naturally leads to the notion of gyrogroups and gyrovector spaces for dealing with the lorentz group and its underlying hyperbolic geometry. they defined the chen addition and then chen model of hyperbolic geometry. in this paper,...

‎In this paper we have introduced new types of sets termed as $omega_{_{gamma_{_mu}}}$-open sets with the help of an operation and a generalized topology‎. ‎We have also defined a notion of $gamma_{_mu}$-Lindel"{o}f spaces and discussed some of its basic properties‎.  

abstract considering the dominance of public open space use, over the use of private open space of single-family housing, in large cities in iran, an important issue in programming for designing open spaces of residential complexes is to facilitate the appropriate development of the children in open spaces. the present paper attempts to provide a flexible framework for tackling the challenge of...