Confluent, locally confluent, and weakly confluent maps

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1972

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Abstract

Certain properties of confluent maps of compacta are developed in this paper, together with some conditions which imply that a map is confluent, A characterization of hereditarily indecomposable continua is given in terms of confluent maps. It is shown that every locally confluent map from a compactum onto a locally connected metric continuum is confluent. This result is used to prove that every locally confluent map from a compactum onto a dendroid is confluent. An example is constructed of two locally confluent maps whose composition is not locally confluent. Finally, it is shown that any map from a metric continuum onto an arc-like continuum is weakly confluent.

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