Document Type

Article

Language

eng

Format of Original

10 p.

Publication Date

2010

Publisher

University of Houston

Source Publication

Houston Journal of Mathematics

Source ISSN

0362-1588

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.

Comments

Published version. Houston Journal of Mathematics, Vol. 36, No. 4 (2010): 1231-1242. Publisher Link. © 2010 University of Houston. Used with permission.

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