Lattices of slowly oscillating functions
General Topology
2025-03-10 v4
Abstract
We show that lattice isomorphisms between lattices of slowly oscillating functions on chain-connected proper metric spaces induce coarsely equivalent homeomorphisms. This result leads to a Banach-Stone-like theorem for these lattices. Furthermore, we provide a representation theorem that characterizes linear lattice isomorphisms among these lattices.
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Cite
@article{arxiv.2405.19555,
title = {Lattices of slowly oscillating functions},
author = {Yutaka Iwamoto},
journal= {arXiv preprint arXiv:2405.19555},
year = {2025}
}
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13 pages