{"paper":{"title":"$P_{Z}(S)$-Metrics and $P_{Z}(S)$-Metric Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Reza Jafarpour-Golzari","submitted_at":"2015-12-29T19:23:04Z","abstract_excerpt":"In this paper, we define notions of $P_{Z}(S)$-metric and $P_{Z}(S)$-metric space and we show that every $P_{Z}(S)$-metric Space, analogous to an ordinary metric space and generally, a $\\Lambda$-metric space, is a topological space, and in continuance, we show that from a topological point of view, some properties of $P_{Z}(S)$-metric spaces, and $\\Lambda$-metric spaces, have coordination."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08760","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"}