Absolute endpoints of chainable continua. (English) Zbl 0655.54024

An endpoint of chainable continuum is a point at which it is always possible to start chaining that continuum. Some endpoints appear to have the property that one is almost “forced” to start (or finish) the chaining at these points. This paper characterizes these “absolute endpoints”, and this characterization is used to show that in a chainable continuum locally connected at p is equivalent to connected im kleinen at p.


54F15 Continua and generalizations
54F50 Topological spaces of dimension \(\leq 1\); curves, dendrites
54D05 Connected and locally connected spaces (general aspects)
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