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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
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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

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