A Weak Topology on Metric Spaces
Armando W. Gutiérrez, Olavi Nevanlinna
Abstract
We use metric functionals to build a weak topology associated with d-weak convergence on metric spaces. We also show the existence of a sequence in the space C[0,1] that is unbounded in the sup-norm yet converges d-weakly. This points out an error in an earlier work.
Create a lesson
Related papers
The Bézout inequality for mixed volumes characterizes simplices
Dylan Langharst, Shouda Wang
Affine dual Minkowski problem for general measures
Cheng Zhang, Hailin Jin
Algebraically independent distances and rigid metrics
Yoshito Ishiki
On the Geometry of Wasserstein Barycenter II: Riemannian Rigidity, Essential Non-Branching, and Finsler Models
Bang-Xian Han, Deng-Yu Liu
Uncentered Blaschke-Santaló inequalities for the Gaussian measure
S. Artstein-Avidan, M. Fradelizi, K. Wyczesany
Hadwiger's classification theorem on the sphere via signed orthoscheme decompositions
Martin Lotz