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Confluent and open retractible continua. (English) Zbl 0928.54033
Summary: A continuum $$X$$ is $$c$$-retractible (resp., $$o$$-retractible) provided that for every subcontinuum $$A$$ of $$X$$ there exists a confluent (resp., open) retraction from $$X$$ onto $$A$$. In this paper we prove that a pathwise $$c$$-retractible continuum is hereditarily locally connected, and a non-degenerate pathwise connected continuum is $$o$$-retractible if and only if it is an arc or a simple closed curve.

##### MSC:
 54F15 Continua and generalizations 54C15 Retraction
continuum
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