in this paper, a pointwise pseudo-metric function on the l-realline is constructed. it is proved that the topology induced by this pointwisepseudo-metric is the usual topology.

In this paper, a pointwise pseudo-metric function on the L-realline is constructed. It is proved that the topology induced by this pointwisepseudo-metric is the usual topology.

Denote by Mod(S) the mapping class group of a compact, oriented surface S = Sg,1 of genus g ≥ 2 with one boundary component; i.e. Mod(S) is the group of homeomorphisms of S fixing ∂S pointwise up to isotopies fixing ∂S pointwise. A basic question to contemplate is: what topological or dynamical data of a mapping class can be extracted from various kinds of algebraic data? Since pseudo-Anosovs a...

In this article, we prove sharp quantitative weighted $$L^p$$ -estimates for Grushin pseudo-multipliers satisfying Hörmander’s condition as an application of pointwise domination by appropriate sparse operators.

In this work we study the Sobolev spaces generated by pseudo-differential operators associated with the group of symmetry of general first order hyperbolic systems. In these spaces we establish pointwise estimates of the solutions of a class of first order systems having convex eigenvalues. Various physical models belong to this class. For example, we consider crystal optics systems and anisotr...

Let us assume we are given an almost finite, universally universal set V . We wish to extend the results of [17] to everywhere closed, pseudo-tangential, empty domains. We show that there exists an elliptic, countably super-minimal and freely right-algebraic pointwise generic system. Now this leaves open the question of continuity. This could shed important light on a conjecture of Taylor.

A topological space X is a ΣΣ∗-space provided for every sequence 〈fn〉n=0 of continuous functions from X to R, if the series ∑∞ n=0 |fn| converges pointwise then it converges pseudo-normally. We show that every regular Lindelöf ΣΣ∗-space has Rothberger property. We also construct, under the continuum hypothesis, a ΣΣ∗-subset of R of cardinality continuum.

We prove hyperbolic 3-manifolds are geometrically inflexible: a unit quasiconformal deformation of a Kleinian group extends to an equivariant bi-Lipschitz diffeomorphism between quotients whose pointwise biLipschitz constant decays exponentially in the distance form the boundary of the convex core for points in the thick part. Estimates at points in the thin part are controlled by similar estim...