A Weak Topology on Metric Spaces
Sep 16, 2026·
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0 min read
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.
Type
Status
Open access
Authors
Research Scientist
I’m a Researcher in Mathematics. I’ve carried out research at Aalto University, Inria Saclay, and VTT. I’ve made contributions to metric geometry, functional analysis and optimization. I’m passionate about quantum computing, risk analysis and optimization algorithms.