A note on Sarkovskii's Theorem in connected linearly ordered spaces

被引:3
作者
Alcaraz, D
Sanchis, M
机构
[1] Univ Politecn Cartagena, Dept Matemat Aplicada & Estadist, Cartagena, Spain
[2] Univ Jaume 1, Dept Matemat, Castellon de La Plana 12071, Spain
来源
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2003年 / 13卷 / 07期
关键词
connected linearly ordered space; Sarkovskii's Theorem; minimal set;
D O I
10.1142/S0218127403007515
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We prove that, for a connected linearly ordered space L, the following conditions are equivalent: (1) L satisfies Sarkovskii's Theorem, (2) there exist turbulent functions on L, and (3) there exists a compact subspace of L which satisfies Sarkovskii's Theorem. Our results are applied in two ways. Firstly, we show that there exist connected linearly ordered spaces without infinite minimal sets; secondly, for each cardinal number A of uncountable cofinality, we construct a connected linearly ordered space L such that: (1) L is a compact nonfirst countable space satisfying Sarkovskii's Theorem, (2) L admits a dense first countable subset, and (3) the density of L is A.
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页码:1665 / 1671
页数:7
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