A Weak Topology on Metric Spaces
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 …
Metric Functionals and Weak Convergence
We introduce a notion of weak convergence in arbitrary metric spaces. Metric functionals are key in our analysis: weak convergence of sequences in a given metric space is tested …
On the Metric Compactification of Infinite Dimensional \(\ell_p\) Spaces
The notion of metric compactification was introduced by Gromov and later rediscovered by Rieffel. It has been mainly studied on proper geodesic metric spaces. We present here a …