Movability and strong Whitney-reversible properties
type: Item
instance of: scholarly article
title: Movability and strong Whitney-reversible properties
zbMATH Open document ID: 0663.54006
DOI: 10.1016/0166-8641(89)90076-X
author: Hisao Kato
published in: Topology and its Applications
publication date: 1989-01-01T00:00:00Z
review text: In [Stud. Topol. Proc. Conf. Charlotte, N. C. 1974, 393-410 (1975; Zbl 0317.54005), Theorem 4 and Example 3], \textit{S. B. Nadler} jun. proved that the property of being locally connected is a sequential strong Whitney- reversible property, and the property of being pathwise connected is not a strong Whitney-reversible property. We show that the property of being (pointed) 1-movable is a sequential strong Whitney-reversible property. As a corollary, the property of being (pointed) movable is a sequential strong Whitney-reversible property for curves. This is an affirmative answer to the author's question in Trans. Am. Math. Soc. 297, 529-546 (1986; Zbl 0607.54014) (5.2). Also, we show that the property of being (nearly) 1-movable is a Whitney property.
Mathematics Subject Classification ID: 54B20
Mathematics Subject Classification ID: 54C56
Mathematics Subject Classification ID: 54F15
zbMATH DE Number: 4084534
zbMATH Keywords: (pointed) 1-movability
zbMATH Keywords: (nearly) 1-movability
zbMATH Keywords: sequential strong Whitney- reversible property
zbMATH Keywords: curves
zbMATH Keywords: Whitney property
MaRDI profile type: Publication
cites work: Q5532996
cites work: Q5640434
cites work: Q5576212
cites work: Hyperspaces of Peano continua are Hubert cubes
cites work: Q4134576
cites work: Q4143889
cites work: Whitney Levels in Hyperspaces of Certain Peano Continua
cites work: Shape Properties of Whitney Maps for Hyperspaces
cites work: Whitney Continua of Curves
cites work: Whitney continua of graphs admit all homotopy types of compact connected ANRs
cites work: Various types of Whitney maps on \(n\)-dimensional compact connected polyhedra (n\(\leq 2)\)
cites work: Movability and homotopy, homology pro-groups of Whitney continua
cites work: Shape Equivalences of Whitney Continua of Curves
cites work: Q3796370
cites work: Hyperspaces of a Continuum
cites work: A note on some strong Whitney-reversible properties
cites work: Shape properties of hyperspaces
cites work: Generalized paths and pointed 1-movability
cites work: Whitney properties
cites work: Q4067781
cites work: Q3425662
cites work: Whitney-reversible properties
cites work: Q4078767
cites work: Contractibility of Whitney continua in C(X)
cites work: Applications of a Vietoris-Begle theorem for multi-valued maps to the cohomology of hyperspaces
cites work: Whitney continua in the hyperspace C(X)
cites work: Extending Whitney maps
cites work: Regular Families of Curves
full work available at URL: 0166-8641(89)90076-x
OpenAlex ID: W2080372703
description: scientific article; zbMATH DE number 4084534