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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
Keywords:
continuum
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