| Title:
|
Mappings related to confluence (English) |
| Author:
|
Charatonik, J. J. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
32 |
| Issue:
|
2 |
| Year:
|
1996 |
| Pages:
|
85-103 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Necessary and sufficient conditions are found in the paper for a mapping between continua to be monotone, confluent, semi-confluent, joining, weakly confluent and pseudo-confluent. Three lists of these conditions are presented. Two are formulated in terms of components and of quasi-components, respectively, of connected closed subsets of the range space, while the third one in terms of connectedness between subsets of the domain space. Some basic relations concerning these concepts are studied. (English) |
| Keyword:
|
confluent |
| Keyword:
|
connected |
| Keyword:
|
continuum |
| Keyword:
|
joining |
| Keyword:
|
mapping |
| Keyword:
|
monotone |
| Keyword:
|
pseudo-confluent |
| Keyword:
|
quasi-component |
| Keyword:
|
semi-confluent |
| Keyword:
|
weakly confluent |
| MSC:
|
54C10 |
| MSC:
|
54F15 |
| idZBL:
|
Zbl 0902.54016 |
| idMR:
|
MR1407341 |
| . |
| Date available:
|
2008-06-06T21:30:19Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107564 |
| . |
| Reference:
|
[E] Engelking, R.: General topology.Heldermann Verlag Berlin, 1989. Zbl 0684.54001, MR 1039321 |
| Reference:
|
[G] Grispolakis, J.: Confluent and related mappings defined by means of quasi-components.Canad. J. Math. 30 (1978), 112-132. Zbl 0376.54004, MR 0481172 |
| Reference:
|
[HY] Hocking, J. G., Young, G. S.: Topology.Addison-Wesley, 1961. MR 0125557 |
| Reference:
|
[K] Kuratowski, K.: Topology.vol. 2, Academic Press and PWN, 1968. Zbl 0849.01044 |
| Reference:
|
[L1] Lelek, A.: On confluent mappings.Colloq. Math. 15 (1966), 223-233. Zbl 0139.40602, MR 0208574 |
| Reference:
|
[L2] Lelek, A.: A classification of mappings pertinent to curve theory.in: Proceedings Univ. Oklahoma Topology Conference 1972, Norman, Oklahoma 1972, 97-103. Zbl 0252.54019, MR 0358667 |
| Reference:
|
[L3] Lelek, A.: Properties of mappings and continua theory.Rocky Mountain J. Math. 6 (1976), 47-59. Zbl 0326.54024, MR 0390996 |
| Reference:
|
[LT] Lelek, A., Tymchatyn, E. D.: Pseudo-confluent mappings and a classification of continua.Canad. J. Math. 27 (1975), 1336-1348. MR 0418022 |
| Reference:
|
[M] Maćkowiak, T.: Continuous mappings on continua.Dissertationes Math. (Rozprawy Mat.) 158 (1979), 1-91. MR 0522934 |
| Reference:
|
[W] Whyburn, G. T.: Analytic topology.Amer. Math. Soc. Colloq. Publ. 28 (1942). Zbl 0061.39301 |
| . |
