Weak chainability of arc folders
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.