José G. Anaya, Enrique Castañeda-Alvarado, José A. Martínez-Cortez
On the hyperspace C_n(X)/{C_n}_K(X)

Comment.Math.Univ.Carolin. 62,2 (2021) 201-224.

Abstract: Let X be a continuum and n a positive integer. Let C_n(X) be the hyperspace of all nonempty closed subsets of X with at most n components, endowed with the Hausdorff metric. For K compact subset of X, define the hyperspace {C_n}_K(X)=\{A\in C_n(X)\colon K\subset A\}. In this paper, we consider the hyperspace C_K^n(X)=C_n(X)/{C_n}_K(X), which can be a tool to study the space C_n(X). We study this hyperspace in the class of finite graphs and in general, we prove some properties such as: aposyndesis, local connectedness, arcwise disconnectedness, and contractibility.

Keywords: hyperspace; continuum; containment hyperspace; aposyndesis; finite graph; Peano continuum; contractibility

DOI: DOI 10.14712/1213-7243.2021.018
AMS Subject Classification: 54B15 54B20 54F15