{"paper":{"title":"Remarks on dimensions of Cartesian product sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Chun Wei, Shengyou Wen, Zhixiong Wen","submitted_at":"2015-01-08T03:02:45Z","abstract_excerpt":"Given metric spaces $E$ and $F$, it is well known that $$\\dim_HE+\\dim_HF\\leq\\dim_H(E\\times F)\\leq\\dim_HE+\\dim_PF,$$ $$\\dim_HE+\\dim_PF\\leq \\dim_P(E\\times F)\\leq\\dim_PE+\\dim_PF,$$ and $$\\underline{\\dim}_BE+\\overline{\\dim}_BF \\leq\\overline{\\dim}_B(E\\times F) \\leq\\overline{\\dim}_BE+\\overline{\\dim}_BF,$$ where $\\dim_HE$, $\\dim_PE$, $\\underline{\\dim}_BE$, $\\overline{\\dim}_BE$ denote the Hausdorff, packing, lower box-counting, and upper box-counting dimension of $E$, respectively. In this note we shall provide examples of compact sets showing that the dimension of the product $E\\times F$ may attain a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01713","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"}