in this paper‎, ‎we introduce a new model of point free topology‎ ‎for point-set topology‎. ‎we study the basic concepts in this‎ ‎structure and will find that it is naturally close to point-set‎ ‎topology‎.‎

In this paper, we define and study fuzzy generalized α-closed sets and r-open sets of a given L-fuzzy topological space and prime element r ∈ P (L) and coprime element α ∈ M(L). The concept of L-fuzzy ropen sets was introduced in [10], and it was proved that all r-open sets for L-fuzzy topological space form a new L-fuzzy topology, which is called stratiform L-fuzzy topology. Making use of the ...

in this paper, the concept of countably near ps-compactness inl-topological spaces is introduced, where l is a completely distributive latticewith an order-reversing involution. countably near ps-compactness is definedfor arbitrary l-subsets and some of its fundamental properties are studied.

Let Σ be the algebraic universal cover of a closed surface of genus g > 1, T (Σ) its Teichmüller space, M(Σ,ℓ) the group of mapping classes stabilizing a fixed leaf ℓ. The L 1 Ehrenpreis conjecture asserts that M(Σ,ℓ) acts on T (Σ) with dense orbits in the L 1 topology (the topology coming from the L 1 norm on quadratic differentials). We give a proof of this weaker version of the Ehrenpreis co...

A frame $L$ is called {it coz-dense} if $Sigma_{coz(alpha)}=emptyset$ implies $alpha=mathbf 0$. Let $mathcal RL$ be the ring of real-valued continuous functions on a coz-dense and completely regular frame $L$. We present a description of the socle of the ring $mathcal RL$ based on minimal ideals of $mathcal RL$ and zero sets in pointfree topology. We show that socle of $mathcal RL$ is an essent...

In 1965 L. A Zadeh [11] introduced fuzzy sets as a generalization of ordinary sets. After that C. L. Chang [2] introduced fuzzy topology and that led to the discussion of various aspects of L-topology by many authors. The Čech closure spaces introduced by Čech E. [1] is a generalization of the topological spaces. The theory of fuzzy closure spaces has been established by Mashhour and Ghanim [4]...

Let L be an Orlicz space defined by a convex Orlicz function φ and let E be the space of finite elements in L (= the ideal of all elements of order continuous norm). We show that the usual norm topology Tφ on L restricted to E can be obtained as an inductive limit topology with respect to some family of other Orlicz spaces. As an application we obtain a characterization of continuity of linear ...