English

Weak topologies for unbounded nets in CAT($0$) spaces

Metric Geometry 2022-04-05 v1

Abstract

Weak topologies that yield weak convergence for bounded sequences and nets in CAT(00) spaces have been studied in the past. We are here concerned with weak topologies that yield weak convergence of unbounded sequences and nets. We analyze two such topologies that generalize the weak topology on Hilbert spaces and that agree with the strong topology on a CAT(00) space if and only if the space is locally compact.

Keywords

Cite

@article{arxiv.2204.01291,
  title  = {Weak topologies for unbounded nets in CAT($0$) spaces},
  author = {Philip Miller and Arian Berdellima and Max Wardetzky},
  journal= {arXiv preprint arXiv:2204.01291},
  year   = {2022}
}
R2 v1 2026-06-24T10:36:35.655Z