Concerning when $F_1(X)$ is a continuum of colocal connectedness in hyperspaces and symmetric products
Volume 160 / 2020
Colloquium Mathematicum 160 (2020), 297-307
MSC: Primary 54B20; Secondary 54F15.
DOI: 10.4064/cm7611-3-2019
Published online: 21 February 2020
Abstract
Given a continuum $X$ and a positive integer $n$, we consider its hyperspaces $2^{X}=\{A\subset X:A$ is closed and nonempty$\}$, $C_n(X)=\{A\in 2^{X}:A$ has at most $n$ components$\}$ and $F_n(X)=\{A\in 2^{X}:A$ has at most $n$ points$\}.$ For a subcontinuum $A$ of $X$ consider the following properties: $A$ is a continuum of colocal connectedness, not weak cut, nonblock, shore, not strong center and noncut in $X$.
We study when $F_1(X)$ has one of these properties in $F_n(X)$, $2^{X}$ or $C_n(X)$.
