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A Note on Open Extension of Maps

Published online by Cambridge University Press:  20 November 2018

J. K. Kohli
J. K. Kohli*
Affiliation:
Indian Institute of Technology Kanpur, Kanpur, India; Hindu College, University of Delhi, Delhi, India
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In recent years there has been some interest in trying to improve the behaviour of maps by extending their domains (see Whyburn [10], Baur [3], Krolevec [8], Dickman [5], Franklin and Kohli [6]). It was shown in [6] that every map can be extended to an open map so that certain properties of the domain and range are preserved in the new domain. In [6] and [7] we also related the topological properties of the domain and range of the mapping with the new domain; also these results were then used to obtain analogues and improvements of recent theorems of Arhangelskii, Čoban, Hodel, Keesling, Nagami, Okuyama, and Proizvolov. In this note we give a method of unifying the domain and range of a mapping so as to yield a meaningful open extension.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 6 , December 1972 , pp. 1139 - 1144
Copyright
Copyright © Canadian Mathematical Society 1972

References

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