Weak chainability of arc folders
Volume 163 / 2021
Colloquium Mathematicum 163 (2021), 211-221
MSC: Primary 54F15, 54B15, 54D80; Secondary 54C10.
DOI: 10.4064/cm7925-2-2020
Published online: 19 June 2020
Abstract
Arc folders are continua that admit mappings onto an arc where the preimage of each point is either an arc or a point. We show that all arc folders are weakly chainable. Equivalently, they are continuous images of the pseudo-arc. We conclude that a continuum $X$ that admits a mapping $f\colon X\to Y$ onto a locally connected continuum $Y$, where the preimage of each point is either an arc or a point, is weakly chainable.
