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Not Every Co-existential Map Is Confluent
| Content Provider | Semantic Scholar |
|---|---|
| Author | Bankston, Paul |
| Copyright Year | 2010 |
| 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 ques- tion 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 the- orems 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 cel- ebrated open problem whether confluent maps preserve chainability, or even being a pseudo-arc; however, as has recently been shown (7), co-existential maps do indeed preserve both these properties. |
| Starting Page | 1233 |
| Ending Page | 1242 |
| Page Count | 10 |
| File Format | PDF HTM / HTML |
| Volume Number | 36 |
| Alternate Webpage(s) | http://www.mscs.mu.edu/~paulb/Paper/conffinal.pdf |
| Alternate Webpage(s) | https://epublications.marquette.edu/cgi/viewcontent.cgi?article=1142&context=mscs_fac |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
