{"paper":{"title":"On Double Sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Huseyin Cakalli, Richard F. Patterson","submitted_at":"2013-12-20T10:27:23Z","abstract_excerpt":"A double sequence $\\{x_{k,l}\\}$ is quasi-Cauchy if given an $\\epsilon > 0$ there exists an $N \\in {\\bf N}$ such that $$\\max_{r,s= 1\\mbox{ and/or} 0} \\left \\{|x_{k,l} - x_{k+r,l+s}|< \\epsilon\\right \\} .$$ We study continuity type properties of factorable double functions defined on a double subset $A\\times A$ of ${\\bf R}^{2}$ into $\\textbf{R}$, and obtain interesting results related to uniform continuity, sequential continuity, continuity, and a newly introduced type of continuity of factorable double functions defined on a double subset $A\\times A$ of ${\\bf R}^{2}$ into $\\textbf{R}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6602","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"}