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Another approach to extensions of continuous mappings

Published online by Cambridge University Press:  17 April 2009

Shu-Hao Sun
Shu-Hao Sun
Affiliation:
Department of Mathematics, Shanghai Institute of Mechanical Engineering, Shanghai, Peoples Republic of China
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Abstract

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First, we give a more general extension theorem about continuous mappings. It is shown that the Taimanov-Eilenberg-Steenrod extension theorem and the Engelking extension theorem are special cases and that this theorem implies the Dugunji extension theorem. The localic version of this theorem also generalises Joyal's extension theorem for locales. Then, using the same technique, we obtain another more interesting extension theorem and its applications. In particular, we sharpen a well-known result due to Wallman.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 39 , Issue 1 , February 1989 , pp. 1 - 9
Copyright
Copyright © Australian Mathematical Society 1989

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