Pseudo-homotopies between maps on g-growth hyperspaces of continua
Volume 170 / 2022
Colloquium Mathematicum 170 (2022), 41-64
MSC: Primary 54F16; Secondary 54C05.
DOI: 10.4064/cm8254-7-2021
Published online: 15 April 2022
Abstract
We introduce the concept of g-growth hyperspace: if $X$ is a continuum, then a non-empty subset $\mathcal H$ of $2^X$ is a g-growth hyperspace of $X$ provided that if $\mathcal A$ is a subcontinuum of $2^X$ and $\mathcal A \cap \mathcal H \neq \emptyset $, then $\bigcup \mathcal A \in \mathcal H$. We study pseudo-homotopies between maps of hyperspaces of continua. As a consequence, we show that pseudo-contractibility and contractibility are equivalent in g-growth hyperspaces.
