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arXiv · 2611.01629

A Banach--Stone-like Theorem for Slowly Oscillating Functions

Yutaka Iwamoto
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Abstract

We prove that every lattice isomorphism between the lattices of slowly oscillating real-valued functions on proper metric spaces induces a coarse homeomorphism. This yields a Banach--Stone-like theorem for slowly oscillating functions, as well as a representation theorem for linear lattice isomorphisms between these function lattices. Both theorems were previously established by the author under the assumption of chain-connectedness. The present paper establishes both results for arbitrary proper metric spaces.

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BibTeXRIS

Yutaka Iwamoto. 2026-11-01. A Banach--Stone-like Theorem for Slowly Oscillating Functions. https://arxiv.org/abs/2611.01629

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