{"paper":{"title":"Detecting topological and Banach fractals among zero-dimensional spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.GN","authors_text":"Filip Strobin, Magdalena Nowak, Taras Banakh","submitted_at":"2015-03-22T07:05:20Z","abstract_excerpt":"A topological space $X$ is called a topological fractal if $X=\\bigcup_{f\\in\\mathcal F}f(X)$ for a finite system $\\mathcal F$ of continuous self-maps of $X$, which is topologically contracting in the sense that for every open cover $\\mathcal U$ of $X$ there is a number $n\\in\\mathbb N$ such that for any functions $f_1,\\dots,f_n\\in \\mathcal F$, the set $f_1\\circ\\dots\\circ f_n(X)$ is contained in some set $U\\in\\mathcal U$. If, in addition, all functions $f\\in\\mathcal F$ have Lipschitz constant $<1$ with respect to some metric generating the topology of $X$, then the space $X$ is called a Banach fr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06396","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"}