Year: 2025
Type: preprint
Abstract: We construct a multiset space $\mathbb{N}[X]$ over a metric space $X$ that simultaneously enjoys desirable topological properties and admits a natural matching metric $d_{\mathbb{N}[X]}$, making it a metrizable abelian topological monoid whose structure is compatible with the original metric on $X$. This framework extends naturally to the free abelian group $\mathbb{Z}[X]$, where a metric $d_{\mathbb{Z}[X]}$ induces a metrizable abelian topological group structure. We further identify the metric completion of $\mathbb{N}[X]$, showing that it carries a canonical extension of the matching metric.
Source: arXiv (Cornell University)
Author: Kim, Donghan
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7091187006
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