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Characterizing dendrites by deformation retractions. (English) Zbl 0890.54037
The main result of the paper says that for a (metric) continuum \(X\) the following assertions are equivalent: (a) \(X\) is a dendrite; (b) each subcontinuum of \(X\) is a deformation retract of \(X\); (c) each subcontinuum of \(X\) is a strong deformation retract of \(X\).
MSC:
54F50 Topological spaces of dimension \(\leq 1\); curves, dendrites
54C15 Retraction
54E40 Special maps on metric spaces
54F15 Continua and generalizations
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