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Approximation and extension of continuous functions

Part of: Linear function spaces and their duals Maps and general types of spaces defined by maps Fairly general properties

Published online by Cambridge University Press:  09 April 2009

Salvador Hernández-Muñoz
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Abstract

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In this paper we study the approximation of vector valued continuous functions defined on a topological space and we apply this study to different problems. Thus we give a new proof of Machado's Theorem. Also we get a short proof of a Theorem of Katětov and we prove a generalization of Tietze's Extension Theorem for vector-valued continuous functions, thereby solving a question left open by Blair.

MSC classification

Secondary: 54C20: Extension of maps 54C30: Real-valued functions 54D60: Realcompactness and realcompactification 46E25: Rings and algebras of continuous, differentiable or analytic functions 54C45: $C$- and $C^*$-embedding 54C99: None of the above, but in this section 46E15: Banach spaces of continuous, differentiable or analytic functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 57 , Issue 2 , October 1994 , pp. 149 - 157
Copyright
Copyright © Australian Mathematical Society 1994

References

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