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 X be a locally convex Hausdorff space (briefly, lcHs) and L(X) denote the space of all continuous linear operators of X into itself. The space L(X) is denoted by Ls(X) when it is equipped with the topology of pointwise convergence in X (i.e. the strong operator topology). By a spectral measure in X is meant a σ-additive map P : Σ → Ls(X), defined on a σ-algebra Σ of subsets of some set Ω, w...

This is a selection of open problems dealing with “large” (non locally compact) topological groups and concerning extreme amenability (fixed point on compacta property), oscillation stability, universal minimal flows and other aspects of universality, and unitary representations. A topological group G is extremely amenable, or has the fixed point on compacta property, if every continuous action...

This is a selection of open problems dealing with “large” (non locally compact) topological groups and concerning extreme amenability (fixed point on compacta property), oscillation stability, universal minimal flows and other aspects of universality, and unitary representations. A topological group G is extremely amenable, or has the fixed point on compacta property, if every continuous action...

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]...