{"paper":{"title":"The wave model of metric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.FA","authors_text":"M. I. Belishev, S. A. Simonov","submitted_at":"2019-01-10T21:22:08Z","abstract_excerpt":"Let $\\Omega$ be a metric space, $A^t$ denote the metric neighborhood of the set $A\\subset\\Omega$ of the radius $t$; ${\\mathfrak O}$ be the lattice of open sets in $\\Omega$ with the partial order $\\subseteq$ and the order convergence. The lattice of $\\mathfrak O$-valued functions of $t\\in(0,\\infty)$ with the point-wise partial order and convergence contains the family ${I\\mathfrak O}=\\{A(\\cdot)\\,|\\,\\,A(t)=A^t,\\,\\,A\\in{\\mathfrak O}\\}$. Let $\\widetilde\\Omega$ be the set of atoms of the order closure $\\overline{I\\mathfrak O}$. We describe a class of spaces for which the set $\\widetilde\\Omega$, equ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.04317","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}