PreprintCC BY 4.0arXiv
A Weak Topology on Metric Spaces
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.
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BibTeX
@misc{gutierrez2026weak,
title = {{A Weak Topology on Metric Spaces}},
author = {Armando W. Gutiérrez and Olavi Nevanlinna},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19368},
eprint = {2609.19368},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19368},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Weak Topology on Metric Spaces
AU - Armando W. Gutiérrez
AU - Olavi Nevanlinna
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.19368
UR - https://arxiv.org/abs/2609.19368
AB - 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.
ER -