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December 2016 On the hyperspace ℭ(X) of continua
R. Escobedo, V. Sánchez-Gutierrez, J. Sánchez-Martínez
Tsukuba J. Math. 40(2): 187-201 (December 2016). DOI: 10.21099/tkbjm/1492104602

Abstract

Let X be a continuum. Let C(X) be the hyperspace of all closed, connected and nonempty subsets of X, with the Hausdorff metric. For a mapping f : XY between continua, let C(f) : C(X) → C(Y) be the induced mapping by f, given by C(f)(A) = f(A). In this paper we study the hyperspace ℭ(X) = {C(A) : AC(X)} as a subspace of C(C(X)), and define an induced function ℭ(f) between ℭ(X) and ℭ(Y). We prove some relationships between the functions f, C(f) and ℭ(f) for the following classes of mapping: confluent, light, monotone and weakly confluent.

Citation

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R. Escobedo. V. Sánchez-Gutierrez. J. Sánchez-Martínez. "On the hyperspace ℭ(X) of continua." Tsukuba J. Math. 40 (2) 187 - 201, December 2016. https://doi.org/10.21099/tkbjm/1492104602

Information

Received: 11 October 2016; Revised: 8 December 2016; Published: December 2016
First available in Project Euclid: 13 April 2017

zbMATH: 06710503
MathSciNet: MR3635384
Digital Object Identifier: 10.21099/tkbjm/1492104602

Subjects:
Primary: 54B10, 54C10, 54F15, 54F65

Rights: Copyright © 2016 University of Tsukuba, Institute of Mathematics

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Vol.40 • No. 2 • December 2016
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