Title

Quotients of n-fold Hyperspaces

Author(s)

Sergio Macías, Universidad Autonoma del Estado de MexicoFollow
Javier Camargo

Document Type

Topology + Dynamics and Continuum Theory

Publication Date

6-2017

Publication Source

32nd Summer Conference on Topology and Its Applications

Abstract

iven a continuum X and an integer n ≥ 2, let C_n(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)=C_n(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(C_n(X))=dim(Cⁿ₁(X)); both Cⁿ₁([0, 1]) and Cⁿ₁(S¹) are Cantor manifolds; etc.

Comments

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Copyright

Copyright © 2017, the Authors

eCommons Citation

Macías, Sergio and Camargo, Javier, "Quotients of n-fold Hyperspaces" (2017). Summer Conference on Topology and Its Applications. 56.
https://ecommons.udayton.edu/topology_conf/56