Tsukuba Journal of Mathematics

Spheres, symmetric products, and quotient of hyperspaces of continua

Enrique Casta;ñeda-Alvarado and Javier Sánchez-Martínez

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Abstract

A continuum means a nonempty, compact and connected metric space. Given a continuum X, the symbols Fn(X) and C1(X) denotes the hyperspace of all subsets of X with at most n points and the hyperspace of subcontinua of X, respectively. If n > 1, we consider the quotient spaces SF1n(X) = Fn(X)/F1(X) and C1(X)/F1(X) obtained by shrinking F1(X) to a point in Fn(X) and C1(X), respectively. In this paper, we study the continua X such that SF1n(X) is homeomorphic to C1(X)/F1(X) and we analyze when the spaces Fn(X) and SF1n(X) are homeomorphic to some sphere.

Article information

Source
Tsukuba J. Math., Volume 38, Number 1 (2014), 75-84.

Dates
First available in Project Euclid: 13 August 2014

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1407938673

Digital Object Identifier
doi:10.21099/tkbjm/1407938673

Mathematical Reviews number (MathSciNet)
MR3261914

Zentralblatt MATH identifier
1304.54035

Subjects
Primary: 54B15: Quotient spaces, decompositions 54B20: Hyperspaces

Keywords
Continuum hyperspace quotient space symmetric product spheres

Citation

Casta;ñeda-Alvarado, Enrique; Sánchez-Martínez, Javier. Spheres, symmetric products, and quotient of hyperspaces of continua. Tsukuba J. Math. 38 (2014), no. 1, 75--84. doi:10.21099/tkbjm/1407938673. https://projecteuclid.org/euclid.tkbjm/1407938673


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