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On Continuous Extensions

On Continuous Extensions We consider various possibilities concerning the continuous extension of continuous functions taking values in an ultrametric space. In Section 1 we consider Tietze-type extension theorems concerning continuous extendibility of continuous functions from compact and closed subsets to the whole space. In Sections 2 and 3 we consider extending “separated” continuous functions in such a way that certain continuous extensions remain separated. Functions taking values in a complete ultravalued field are dealt with in Section 2, and the real and complex cases in Section 3. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

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Publisher
de Gruyter
Copyright
© 1996 Plenum Publishing Corporation
ISSN
1072-947X
eISSN
1072-9176
DOI
10.1515/GMJ.1996.565
Publisher site
See Article on Publisher Site

Abstract

We consider various possibilities concerning the continuous extension of continuous functions taking values in an ultrametric space. In Section 1 we consider Tietze-type extension theorems concerning continuous extendibility of continuous functions from compact and closed subsets to the whole space. In Sections 2 and 3 we consider extending “separated” continuous functions in such a way that certain continuous extensions remain separated. Functions taking values in a complete ultravalued field are dealt with in Section 2, and the real and complex cases in Section 3.

Journal

Georgian Mathematical Journalde Gruyter

Published: Dec 1, 1996

Keywords: Continuous extension; Tietze extension theorem

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