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.
Recommended Citation
Bankston, Paul, "Not Every Co-existential Map is Confluent" (2010). Mathematics, Statistics and Computer Science Faculty Research and Publications. 142.
https://epublications.marquette.edu/mscs_fac/142
Comments
Published version. Houston Journal of Mathematics, Vol. 36, No. 4 (2010): 1231-1242. Publisher Link. © 2010 University of Houston. Used with permission.