Soit M une surface fermée connexe orientable sans bord et f un homéomorphisme de M. Supposons que lʼensemble soit fermé. Alors la suspension vérifie lʼune des conditions suivantes : 1) lʼadhérence dʼun élément est un tore ; 2) il existe un ensemble minimal qui nʼest pas localement connexe. De plus, on démontre que si lʼensemble dʼun homéomorphisme f dʼun espace compact métrisable est fermé, alors les sont fermés pour tout entier naturel k.
Let M be an orientable connected closed surface and f be a homeomorphism on M. Suppose that the set is closed. Then the suspension of f satisfies one of the following conditions: 1) the closure of each element of it is toral; 2) there is a minimal set which is not locally connected. Moreover, we show that if the set of a homeomorphism f on a compact metrizable space is closed, then so is for any natural number k.
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@article{CRMATH_2012__350_23-24_1051_0, author = {Yokoyama, Tomoo}, title = {Minimal sets of {\protect\emph{R}-closed} surface homeomorphisms}, journal = {Comptes Rendus. Math\'ematique}, pages = {1051--1053}, publisher = {Elsevier}, volume = {350}, number = {23-24}, year = {2012}, doi = {10.1016/j.crma.2012.11.002}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2012.11.002/} }
TY - JOUR AU - Yokoyama, Tomoo TI - Minimal sets of R-closed surface homeomorphisms JO - Comptes Rendus. Mathématique PY - 2012 SP - 1051 EP - 1053 VL - 350 IS - 23-24 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2012.11.002/ DO - 10.1016/j.crma.2012.11.002 LA - en ID - CRMATH_2012__350_23-24_1051_0 ER -
%0 Journal Article %A Yokoyama, Tomoo %T Minimal sets of R-closed surface homeomorphisms %J Comptes Rendus. Mathématique %D 2012 %P 1051-1053 %V 350 %N 23-24 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2012.11.002/ %R 10.1016/j.crma.2012.11.002 %G en %F CRMATH_2012__350_23-24_1051_0
Yokoyama, Tomoo. Minimal sets of R-closed surface homeomorphisms. Comptes Rendus. Mathématique, Tome 350 (2012) no. 23-24, pp. 1051-1053. doi : 10.1016/j.crma.2012.11.002. http://www.numdam.org/articles/10.1016/j.crma.2012.11.002/
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