{"paper":{"title":"$delta$-Quasi Cauchy Sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.GN"],"primary_cat":"math.FA","authors_text":"Huseyin Cakalli","submitted_at":"2010-05-26T20:11:02Z","abstract_excerpt":"Recently, a concept of forward continuity and a concept of forward compactness are introduced in the senses that a function $f$ is forward continuous if $\\lim_{n\\to\\infty} \\Delta f(x_{n})=0$ whenever $\\lim_{n\\to\\infty} \\Delta x_{n}=0$,\\; and a subset $E$ of $\\textbf{R}$ is forward compact if any sequence $\\textbf{x}=(x_{n})$ of points in $E$ has a subsequence $\\textbf{z}=(z_{k})=(x_{n_{k}})$ of the sequence $\\textbf{x}$ such that $\\lim_{k\\to \\infty} \\Delta z_{k}=0$ where $\\Delta z_{k}=z_{k+1}-z_{k}$. These concepts suggest us to introduce a concept of second forward continuity in the sense tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.4940","kind":"arxiv","version":3},"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"}