• Not every co-existential map is confluent, Vol 36, No.4

Bankston, Paul, Mathematics, Statistics and Computer Science, Marquette University, Milwaukee, WI 53201 (paulb@mscs.mu.edu).
Not every co-existential map is confluent, pp. 1233-1242.
ABSTRACT. A continuous surjection between compacta is co-existential if it is the second of two maps whose composition is a standard ultracopower projection. Co-existential maps are always weakly confluent, and are even monotone when the range space is locally connected; so it is a natural question to ask whether they are always confluent. Here we give a negative answer. This is an interesting question, mainly because of the fact that most theorems about confluent maps have parallel versions for co-existential maps---notably, both kinds of maps preserve hereditary indecomposability. Where the known parallels break down is in the question of chainability. It is a celebrated open problem whether confluent maps preserve chainability, or even being a pseudo-arc; however, as has recently been shown, co-existential maps do indeed preserve both these properties.

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Not every co-existential map is confluent, Vol 36, No.4

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