Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-26T01:06:35.975Z Has data issue: false hasContentIssue false
  • English
  • Français

Confluent and Related Mappings Defined by Means of Quasi-Components

Published online by Cambridge University Press:  20 November 2018

Joachim Grispolakis
Joachim Grispolakis*
Affiliation:
University of Saskatchewan, Saskatoon, Saskatchewan
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In 1964, J. J. Charatonik in [1] introduced a new class of mappings, the so-called confluent mappings, which comprises the classes of open, monotone and quasi-interior mappings (see [20]). In 1966, A. Lelek started working on confluent mappings with applications to continua theory (see [7]). He introduced two other classes of mappings, the so-called weakly confluent and pseudo confluent mappings, he proved the invariance of rational continua under open, monotone and quasi-interior mappings and he asked about their invariance under confluent mappings. In 1976, E. D. Tymchatyn gave an example of a confluent mapping, which does not preserve the rationality of a curve (see [18]).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 1 , 01 February 1978 , pp. 112 - 132
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Charatonik, J. J., Confluent mappings and unicoherence of continua, Fund. Math. 56 (1964).Google Scholar
2. Grispolakis, J., Lelek, A. and Tymchatyn, E. D., Connected subsets of finitely Suslinian continua, Colloq. Math. 35 (1976), 31–44.Google Scholar
3. Grispolakis, J., On a problem of Lelek concerning open mappings, to appear, Colloq. Math.Google Scholar
4. Kuratowski, K., Topology I (Academic Press, New York, 1966).Google Scholar
5. Kuratowski, K., Topology II (Academic Press, New York, 1968).Google Scholar
6. Lelek, A., Ensembles a-connexes et le théorème de Gehman, Fund. Math. I±7 (1959), 265–276.Google Scholar
7. Lelek, A., On confluent mappings, Colloq. Math. 15 (1966), 223–233.Google Scholar
8. Lelek, A., Some problems concerning curves, Colloq. Math. 23 (1971), 93–98.Google Scholar
9. Lelek, A., Some union theorems for confluent mappings, Colloq. Math. 31 (1974), 57–65.Google Scholar
10. Lelek, A. and Read, D. R., Compositions of confluent mappings and some other classes of functions, Colloq. Math. 29 (1974), 101–112.Google Scholar
11. Lelek, A. and Tymchatyn, E. D., Pseudo confluent mappings and a classification of continua theory, Can. J. Math. 27 (1975), 1336–1348.Google Scholar
12. Lelek, A., Properties of mappings and continua theory, Rocky Mountain J. Math. 6 (1976), 47–59.Google Scholar
13. Lelek, A., The M-mappings of continua, to appear.Google Scholar
14. Mackowiak, T., Continuous mappings on continua, to appear.Google Scholar
15. Nishiura, T., Tymchatyn, E. D., Hereditarily locally connected spaces, Houston J. Math. 2 (1976), 581–599.Google Scholar
16. Read, D. R., Confluent, locally confluent, and weakly confluent maps, Dissertation, University of Houston (1972).Google Scholar
17. Rudy, Z., Some properties of the product of mappings, Bull. Acad. Polon. Sci. Math. Astron. Phys., to appear.Google Scholar
18. Tymchatyn, E. D., Some rational continua, to appear.Google Scholar
19. Whyburn, G. T., Analytic Topology, A.M.S. Colloquium Publications #£ (1942).Google Scholar
20. Whyburn, G. T., Open mappings of locally compact spaces, A.M.S. Memoirs 1 (1950).Google Scholar