Boundary sets for growth hyperspaces
type: Item
instance of: scholarly article
title: Boundary sets for growth hyperspaces
zbMATH Open document ID: 0627.54004
DOI: 10.1016/0166-8641(87)90083-6
author: Doug Curtis
author: Mark Michael
published in: Topology and its Applications
publication date: 1987-01-01T00:00:00Z
review text: A subspace G of the hyperspace \(2^ X\) of the Peano continuum X is called a growth hyperspace if G contains every order arc A in \(2^ X\) such that \(\cap A\in G\). If G and H are growth hyperspaces of \(2^ X\) such that H is compact, G is a \(\sigma\)-compact dense subset of H, and the identity map on H can be approximated by continuous maps of H into H- G, then G is called a growth boundary set for H. It is known that H is homeomorphic to the Hilbert cube and that H-G is homeomorphic to Hilbert space. The authors investigate the existence and properties of growth boundary sets for certain growth hyperspaces. They are particularly interested in growth boundary sets which are cap sets or f-d cap sets. The definitions of these sets are too technical to be given here.
Mathematics Subject Classification ID: 54B20
Mathematics Subject Classification ID: 54F15
Mathematics Subject Classification ID: 57N20
zbMATH DE Number: 4019972
zbMATH Keywords: growth hyperspaces of Peano continua
zbMATH Keywords: growth boundary set
zbMATH Keywords: Hilbert cube
zbMATH Keywords: Hilbert space
zbMATH Keywords: f-d cap sets
MaRDI profile type: Publication
full work available at URL: 0166-8641(87)90083-6
OpenAlex ID: W2016406574
cites work: Estimated extension theorem, homogeneous collections and skeletons and their applications to topological classification of linear metric spaces and convex sets
cites work: Q4060144
cites work: Partitioning a set
cites work: Dense Sigma-Compact Subsets of Infinite-Dimensional Manifolds
cites work: Hyperspaces which characterize simple homotopy type
cites work: Hyperspaces of Peano continua are Hubert cubes
cites work: Growth Hyperspaces of Peano Continua
cites work: Q3868444
cites work: Boundary sets in the Hilbert cube
cites work: Hyperspaces of finite subsets as boundary sets
cites work: Examples of cell-like decompositions of the infinite-dimensional manifolds sigma and Sigma
cites work: Hyperspaces of a Continuum
cites work: Q4104540
cites work: Q3906090
cites work: Grille decomposition and convexification theorems for compact metric locally connected continua
cites work: Q5601316
cites work: On CE-images of the Hubert cube and characterization of Q-manifolds
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description: scientific article; zbMATH DE number 4019972