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Weak chainability of arc folders. (English) Zbl 1457.54027

Summary: 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 \(f:X\to Y\) onto a locally connected continuum \(Y\), where the preimage of each point is either an arc or a point, is weakly chainable.

MSC:

54F15 Continua and generalizations
54B15 Quotient spaces, decompositions in general topology
54D80 Special constructions of topological spaces (spaces of ultrafilters, etc.)
54C10 Special maps on topological spaces (open, closed, perfect, etc.)
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