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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
##### Keywords:
continuum; dendrite; strong deformation retract
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