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Pseudo-Confluent Mappings and a Classification of Continua

Published online by Cambridge University Press:  20 November 2018

A. Lelek
Affiliation:
Wayne State University, Detroit, Michigan
E. D. Tymchatyn
Affiliation:
University of Saskatchewan, Saskatoon, Saskatchewan
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In this paper we introduce a new class of mappings and apply it to study some local properties of continua. A solution is obtained to a problem raised in [14] by the first author (see 4.4 below). By a mapping we always mean a continuous function.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Charatonik, J. J., Confluent mappings and unicoherence of continua, Fund. Math. 56 (1964), 213220.Google Scholar
2. Gordh, C. A., Fugate, J. B. and Eberhart, G. R. Jr., Branch-point covering theorems for confluent and weakly confluent mappings, to appear.Google Scholar
3. Epps, B. B. Jr., Strongly confluent mappings, Notices Amer. Math. Soc. 19 (1972), A-807.Google Scholar
4. Epps, B. B., A classification of continua and confluent transformations, Ph.D. thesis, University of Houston, 1973.Google Scholar
5. Fort, M. K. Jr., Images of plane continua, Amer. J. Math. 81 (1959), 541546.Google Scholar
6. Jobe, J., Dendrites, dimension, and the inverse arc function, Pacific J. Math. 1+5 (1973), 245256.Google Scholar
7. Krasinkiewicz, J., Remark on mappings not raising dimension of curves, Pacific J. Math. 55 (1974), 479481.Google Scholar
8. Kuratowski, K., Topology, vol. I (Academic Press 1966).Google Scholar
9. Kuratowski, K., Topology, vol. II (Academic Press 1968).Google Scholar
10. Lelek, A., On confluent mappings, Colloq. Math. 15 (1966), 223233.Google Scholar
11. Lelek, A., On the topology of curves II, Fund. Math. 70 (1971), 131138.Google Scholar
12. Lelek, A., A classification of mappings pertinent to curve theory, Proc. Univ. Oklahoma Topology Conference 1972, 97103.Google Scholar
13. Lelek, A., Report on weakly confluent mappings, Proc. Virginia Polytechnic Institute State Univ. Topology Conference 1973; Lecture Notes in Mathematics 375, Springer-Verlag 1974, 168170.Google Scholar
14. Lelek, A., Several problems of continua theory, Proc. Univ. North Carolina Charlotte Topology Conference 1974; Studies in Topology, Academic Press 1975, 325329.Google Scholar
15. Lelek, A., Properties of mappings and continua theory, to appear, Rocky Mountain J. Math.Google Scholar
16. Lelek, A., Some rational curves and properties of mappings, to appear, Colloq. Math.Google Scholar
17. Lelek, A. and Read, D. R., Compositions of confluent mappings and some sup>her classes of functions, Colloq. Math. 29 (1974), 101112.her+classes+of+functions,+Colloq.+Math.+29+(1974),+101–112.>Google Scholar
18. Mazurkiewicz, S., Sur Vexistence des continus indécomposables, Fund. Math. 25 (1935), 327328.Google Scholar
19. Tymchatyn, E. D., Continua in which all connected subsets are arcwise connected, Trans. Amer. Math. Soc. 205 (1975), 317331.Google Scholar
20. Whyburn, G. T., Analytic topology, Amer. Math. Soc. Colloquium Publications, vol. 28, 1963.Google Scholar