This article gives results on fixed basis frame valued neighborhood topological groups and stratified neighborhood topological groups, includes some characterization theorems, and presents the uniformizability of stratified neighborhood topological groups within the unified approach of Gutiérrez García, DePrada Vicente, and Šostak. It is shown that for a frame L, the category L-NGrp is topologi...

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]...

We prove that any steady solution to the Cω Euler equations on a Riemannian S3 must possess a periodic orbit bounding an embedded disc. One key ingredient is an extension of Fomenko’s work on the topology of integrable Hamiltonian systems to a degenerate case involving stratified integrals. The result on the Euler equations follows from this when combined with some contact-topological perspecti...

This is a glossary of notions and methods related with the topological theory of collections of affine planes, including braid groups, configuration spaces, order complexes, stratified Morse theory, simplicial resolutions, complexes of graphs, Orlik– Solomon rings, Salvetti complex, matroids, Spanier–Whitehead duality, twisted homology groups, monodromy theory and multidimensional hypergeometri...

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 ...