Connectedness and inverse limits with set -valued functions on intervals

被引：9

作者：

Greenwood, Sina ^{[1
]}

Kennedy, Judy ^{[2
]}

Lockyer, Michael ^{[1
]}

机构：

[1] Univ Auckland, Private Bag 92019, Auckland, New Zealand

[2] Lamar Univ, Dept Math, POB 10047, Beaumont, TX 77710 USA

来源：

TOPOLOGY AND ITS APPLICATIONS | 2017年 / 221卷

关键词：

Generalised inverse limit; Connected; Compact; CC-sequence; Component base;

D O I：

10.1016/j.topol.2017.01.011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In [4] it was shown that an inverse limit with upper semicontinuous set-valued functions on intervals is connected if and only if it does not admit a CC-sequence. We introduce a related notion, a component base. Using this new tool we demonstrate how proofs of connectedness theorems can be simplified, and we prove a number of new results on connectedness. In particular, results relating to the size and number of components. (C) 2017 Elsevier B.V. All rights reserved.

引用

页码：69 / 90

页数：22

共 50 条

[1] A characterisation of the dimension of inverse limits of set-valued functions on intervals
Banic, Iztok
Greenwood, Sina
FUNDAMENTA MATHEMATICAE, 2020, 249 (01) : 1 - 19
[2] INVERSE LIMITS WITH SET VALUED FUNCTIONS
Nall, Van
HOUSTON JOURNAL OF MATHEMATICS, 2011, 37 (04): : 1323 - 1332
[3] 2-MANIFOLDS AND INVERSE LIMITS OF SET-VALUED FUNCTIONS ON INTERVALS
Greenwood, Sina
Suabedissen, Rolf
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2017, 37 (11) : 5693 - 5706
[4] Path-connected inverse limits of set-valued functions on intervals
Greenwood, Sina
Lockyer, Michael
TOPOLOGY AND ITS APPLICATIONS, 2020, 280
[5] MARKOV-LIKE SET-VALUED FUNCTIONS ON INTERVALS AND THEIR INVERSE LIMITS
Imamura, Hayato
GLASNIK MATEMATICKI, 2018, 53 (02) : 385 - 401
[6] Indecomposability in inverse limits with set-valued functions
Kelly, James P.
Meddaugh, Jonathan
TOPOLOGY AND ITS APPLICATIONS, 2013, 160 (13) : 1720 - 1731
[7] Inverse limits of families of set-valued functions
Ingram, W. T.
BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA, 2015, 21 (01): : 53 - 70
[8] Confluent set-valued functions and inverse limits
Juarez-Villa, Leonardo
Puga, Isabel
TOPOLOGY AND ITS APPLICATIONS, 2020, 276
[9] Inverse limits of families of set-valued functions
W. T. Ingram
Boletín de la Sociedad Matemática Mexicana, 2015, 21 (1) : 53 - 70
[10] Markov set-valued functions and their inverse limits
Alvin, Lori
Kelly, James P.
TOPOLOGY AND ITS APPLICATIONS, 2018, 241 : 102 - 114

← 1 2 3 4 5 →