{"paper":{"title":"Topological Structure of Fractal Squares","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GT","math.MG"],"primary_cat":"math.GN","authors_text":"Hui Rao, Jun Jason Luo, Ka-Sing Lau","submitted_at":"2012-06-21T10:26:35Z","abstract_excerpt":"Given an integer $n\\geq 2$ and a digit set ${\\mathcal D}\\subsetneq {0,1,...,n-1}^2$, there is a self-similar set $F \\subset {\\Bbb R}^2$ satisfying the set equation: $F=(F+{\\mathcal D})/n$. We call such $F$ a fractal square. By studying a periodic extension $H= F+ {\\mathbb Z}^2$, we classify $F$ into three types according to their topological properties. We also provide some simple criteria for such classification."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.4826","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"}