{"paper":{"title":"Discontinuous maps whose iterations are continuous","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.GT","authors_text":"Kouki Taniyama","submitted_at":"2013-10-07T14:48:34Z","abstract_excerpt":"Let $X$ be a topological space and $f:X\\to X$ a bijection. Let ${\\mathcal C}(X,f)$ be a set of integers such that an integer $n$ is an element of ${\\mathcal C}(X,f)$ if and only if the bijection $f^n:X\\to X$ is continuous. A subset $S$ of the set of integers ${\\mathbb Z}$ is said to be realizable if there is a topological space $X$ and a bijection $f:X\\to X$ such that $S={\\mathcal C}(X,f)$. A subset $S$ of ${\\mathbb Z}$ containing 0 is called a submonoid of ${\\mathbb Z}$ if the sum of any two elements of $S$ is also an element of $S$. We show that a subset $S$ of ${\\mathbb Z}$ is realizable if"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1804","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"}