Description

• Title:
  Subspaces of interval maps related to the topological entropy
• Creator:
  Fan, Xiaoxin;
  Li, Jian;
  Yang, Yini;
  Yang, Zhongqiang
• Description:
  For $a\in [0,+\infty)$, the function space $E_{\geq a}$ ($E_{> a}$; $E_{\leq a}$; $E_{< a}$) of all continuous maps from $[0,1]$ to itself whose topological entropies are larger than or equal to $a$ (larger than $a$; smaller than or equal to $a$; smaller than $a$) with the supremum metric is investigated. It is shown that the spaces $E_{\geq a}$ and $E_{> a}$ are homeomorphic to the Hilbert space $l_2$ and the spaces $E_{\leq a}$ and $E_{< a}$ are contractible. Moreover, the subspaces of $E_{\leq a}$ and $E_{< a}$ consisting of all piecewise monotone maps are homotopy dense in them, respectively.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2019 Topological Methods in Nonlinear Analysis
• Date:
  2019.10.06
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 54, No 2 (December 2019); 701 - 714;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2019.065/18482 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2019.065/18483
• Subject:
  Interval maps;
  topological entropy;
  the Hilbert space $l_2$;
  homotopy dense;
  contractible;
  Primary;
  37E05;
  54F65;
  Secondary;
  54H20
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2019.065
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other