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Boundary sets for growth hyperspaces. (English) Zbl 0627.54004
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.
Reviewer: B.J.Pearson

54B20 Hyperspaces in general topology
54F15 Continua and generalizations
57N20 Topology of infinite-dimensional manifolds
Full Text: DOI
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