{"paper":{"title":"On strong spaceability of continuous functions and fractal dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jia Liu, Saisai Shi, Zhenliang Zhang","submitted_at":"2026-05-24T12:25:01Z","abstract_excerpt":"Given $s\\in(1,2]$, define $$H_s[0,1]=\\{f\\in C[0,1]:{\\dim}_HG_f([0,1])=s\\}$$ and $$\\overline{B}_s[0,1]=\\{f\\in C[0,1]:\\overline{{\\dim}}_BG_f([0,1])=s\\}.$$ The main goal of this paper is to study the $(\\alpha,\\beta)$-lineability/spaceability of the sets $H_s[0,1]$ and $\\overline{B}_s[0,1]$. As a principle result, we prove that $H_s[0,1]$ is $(p,\\mathfrak{c})$-spaceable for $p=1,2$ and also $(n,n+m)$-lineable for any $m,n\\in\\mathbb{N}$. This partially answers a question raised by Liu et al. concerning the Hausdorff dimension of graphs of continuous functions.\n  Furthermore, for a cardinal number $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25037","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.25037/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}