{"paper":{"title":"$\\mathcal I^{\\mathcal K}$-Cauchy functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Martin Sleziak, Pratulananda Das, Vladim\\'ir Toma","submitted_at":"2013-12-29T12:19:57Z","abstract_excerpt":"In this paper we introduce the notion of $\\mathcal I^{\\mathcal K}$-Cauchy function, where $\\mathcal I$ and $\\mathcal K$ are ideals on the same set. The $\\mathcal I^{\\mathcal K}$-Cauchy functions are a generalization of $\\mathcal I^*$-Cauchy sequences and $\\mathcal I^*$-Cauchy nets. We show how this notion can be used to characterize complete uniform spaces and we study how $\\mathcal I^{\\mathcal K}$-Cauchy functions and $\\mathcal I$-Cauchy functions are related. We also define and study $\\mathcal I^{\\mathcal K}$-divergence of functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7527","kind":"arxiv","version":2},"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"}