Topology + Dynamics and Continuum Theory
32nd Summer Conference on Topology and Its Applications
iven a continuum X and an integer n ≥ 2, let Cn(X) be the n-fold hyperspace of X consisting of all nonempty closed subsets of X with at most n components. We consider the quotient space Cn1(X)=Cn(X)/C1(X) with the quotient topology. We prove several properties. For example: Cn1(X) is unicoherent; if X has the property of Kelley, Cn1(X) is contractible; dim(Cn(X))=dim(Cn1(X)); both Cn1([0, 1]) and Cn1(S1) are Cantor manifolds; etc.
Copyright © 2017, the Authors
Macías, Sergio and Camargo, Javier, "Quotients of n-fold Hyperspaces" (2017). Summer Conference on Topology and Its Applications. 56.