{"paper":{"title":"On G-Continuity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Huseyin Cakalli","submitted_at":"2010-06-24T07:47:34Z","abstract_excerpt":"A function $f$ on a topological space is sequentially continuous at a point $u$ if, given a sequence $(x_{n})$, $\\lim x_{n}=u$ implies that $\\lim f(x_{n})=f(u)$. This definition was modified by Connor and Grosse-Erdmann for real functions by replacing $lim$ with an arbitrary linear functional $G$ defined on a linear subspace of the vector space of all real sequences. In this paper, we extend this definition to a topological group $X$ by replacing $G$ a linear functional with an arbitrary additive function defined on a subgroup of the group of all $X$-valued sequences and not only give new theo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.4706","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"}