Summer Conference on Topology and Its Applications

Document Type

Topology + Dynamics and Continuum Theory

Publication Date


Publication Source

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.


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