{"paper":{"title":"On the imbedding of a finite family of closed disks into a plane or S^{2}","license":"","headline":"","cross_cats":["math.AT","math.MG"],"primary_cat":"math.GT","authors_text":"Eugene Polulyakh","submitted_at":"1999-10-21T10:52:49Z","abstract_excerpt":"Let $\\{V_{i}\\}_{i=1}^{n}$ be a finite family of closed subsets of a plane or a sphere $S^{2}$, each homeomorphic to the two-dimensional disk. In this paper we discuss the question how the boundary of connected components of a complement $\\rr^{2} \\setminus \\bigcup_{i=1}^{n} V_{i}$ (accordingly, $S^{2} \\setminus \\bigcup_{i=1}^{n} V_{i}$) is arranged.\n  It appears, if a set $\\bigcup_{i=1}^{n} \\Int V_{i}$ is connected, that the boundary $\\partial W$ of every connected component $W$ of the set $\\rr^{2} \\setminus \\bigcup_{i=1}^{n} V_{i}$ (accordingly, $S^{2} \\setminus \\bigcup_{i=1}^{n} V_{i}$) is ho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9910108","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"}