{"paper":{"title":"Extended by Balk metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"D. Dordovskyi, O. Dovgoshey","submitted_at":"2013-10-13T08:04:44Z","abstract_excerpt":"Let $X$ be a nonempty set and $\\mathcal{F}(X)$ be the set of nonempty finite subsets of $X$. The paper deals with the extended metrics $\\tau:\\mathcal{F}(X)\\to\\mathbb{R}$ recently introduced by Peter Balk. Balk's metrics and their restriction to the family of sets $A$ with $|A|\\leqslant n$ make possible to consider \"distance functions\" with $n$ variables and related them quantities. In particular, we study such type generalized diameters $\\diam_{\\tau^n}$ and find conditions under which $B\\mapsto\\diam_{\\tau^n}B$ is a Balk's metric. We prove the necessary and sufficient conditions under which the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3456","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"}