Isomorphism of almost locally compact Polish metric structures

Maciej Malicki

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arXiv · 2508.07765

Isomorphism of almost locally compact Polish metric structures

Maciej Malicki

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Abstract

A topological space is almost locally compact if it contains a dense locally compact subspace. We generalize a result from \cite{Ma}, showing that isomorphism on Borel classes of almost locally compact Polish metric structures is always classifiable by countable structures. This allows to remove a gap in the proof presented in \cite{Ma} of a positive answer to a question of Gao and Kechris, who asked whether isometry of locally compact Polish metric spaces is classifiable by countable structures.

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BibTeX RIS

Maciej Malicki. 2025-08-11. Isomorphism of almost locally compact Polish metric structures. https://arxiv.org/abs/2508.07765

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