Abstract
Chapter 1 is intended to give the reader a fairly clear introduction to Part 3 of the book (Chapters 5{8) devoted to extensions of Lipschitz maps between metric spaces. This will be done on the basis of methods and results regarded as \classical" in this rather young field of modern analysis. The matter on continuous functions presented is used to motivate the problems and methods that will be developed in Part 3. For instance, topological theory relating (covering) dimension and continuous extensions of maps into spheres (Theorem 1.9 and Appendix A) has a metric counterpart (Chapter 6) with Nagata dimension substituted for the covering one.
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© 2012 Springer Basel AG
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Brudnyi, A., Brudnyi, Y. (2012). Continuous and Lipschitz Functions. In: Methods of Geometric Analysis in Extension and Trace Problems. Monographs in Mathematics, vol 102. Springer, Basel. https://doi.org/10.1007/978-3-0348-0209-3_1
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DOI: https://doi.org/10.1007/978-3-0348-0209-3_1
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Publisher Name: Springer, Basel
Print ISBN: 978-3-0348-0208-6
Online ISBN: 978-3-0348-0209-3
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