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Soc."],"published-print":{"date-parts":[[2024,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We prove that every homeomorphism of a compact manifold with dimension one has zero topological emergence, whereas in dimension greater than one the topological emergence of a <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0305004124000343_inline1.png\"\/><jats:tex-math>\n$C^0-$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>generic homeomorphism is maximal, equal to the dimension of the manifold. We also show that the metric emergence of a continuous self-map on compact metric space has the intermediate value property.<\/jats:p>","DOI":"10.1017\/s0305004124000343","type":"journal-article","created":{"date-parts":[[2024,12,27]],"date-time":"2024-12-27T06:01:07Z","timestamp":1735279267000},"page":"525-551","source":"Crossref","is-referenced-by-count":0,"title":["Topological and metric emergence of continuous maps"],"prefix":"10.1017","volume":"177","author":[{"given":"MARIA","family":"CARVALHO","sequence":"first","affiliation":[]},{"given":"FAGNER B.","family":"RODRIGUES","sequence":"additional","affiliation":[]},{"given":"PAULO","family":"VARANDAS","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2024,12,27]]},"reference":[{"key":"S0305004124000343_ref14","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0103945"},{"key":"S0305004124000343_ref6","doi-asserted-by":"crossref","unstructured":"[6] Bowen, R. . 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