Pseudo-endpoints of chainable continua and endpoints of nondegenerate hereditarily decomposable chainable continua

Date

2018-08

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Abstract

We present a characterization of pseudo-endpoints of chainable continua. We then use this to show that confluent maps between chainable continua preserve pseudo-endpoints. This characterization gives an affirmative answer to the following question by J.J Charatonik and T. Mackowiak. "Do confluent mappings between arc-like (chainable) continua preserve pseudo-endpoints?"([2],4.6 problem)

Then we use this to give a new proof (easy) to the known result "A nondegenerate chainable continuum X is the pseudo-arc if and only if it is homogeneous with respect to the class of confluent mappings."

Then we use the same proof technique and partially answer a question raised by J.J Charatonik [4] (page 902) by extending the known results.

Further we use the concept of pseudo-endpoint to show that an hereditarily decomposable chainable continuum must have a pair of endpoints and to investigate further results concerning endpoints of hereditairy decomposable chainable continua.

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Keywords

Pseudo-endpoints, Endpoints, Chainable continua, Hereditarily decomposable, Confluent, Pseudo-arc, Generalized homogeneity

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