Lattice projections on continuous function spaces

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

Function Spaces of Posets with Projections

Continuous Quotients for Lattice Actions on Compact Spaces

Let Γ < SLn(Z) be a subgroup of finite index, where n≥5. Suppose Γ acts continuously on a manifold M , where π1(M) = Z n, preserving a measure that is positive on open sets. Further assume that the induced Γ action on H(M) is non-trivial. We show there exists a finite index subgroup Γ′ < Γ and a Γ′ equivariant continuous map ψ :M→Tn that induces an isomorphism on fundamental group. We prove mor...

ON STRATIFIED LATTICE-VALUED CONVERGENCE SPACES

In this paper we provide a common framework for different stratified $LM$-convergence spaces introduced recently. To this end, we slightly alter the definition of a stratified $LMN$-convergence tower space. We briefly discuss the categorical properties and show that the category of these spaces is a Cartesian closed and extensional topological category. We also study the relationship of our cat...

On projections of metric spaces

Let X be a metric space and let μ be a probability measure on it. Consider a Lipschitz map T : X → Rn, with Lipschitz constant ≤ 1. Then one can ask whether the image TX can have large projections on many directions. For a large class of spaces X, we show that there are directions φ ∈ Sn−1 on which the projection of the image TX is small on the average (in L2(μ)), with bounds depending on the d...