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.
Citation
Enrique Casta;ñeda-Alvarado. Javier Sánchez-Martínez. "Spheres, symmetric products, and quotient of hyperspaces of continua." Tsukuba J. Math. 38 (1) 75 - 84, July 2014. https://doi.org/10.21099/tkbjm/1407938673
Information