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 : X → Y 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) : A ∈ C(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
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
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