Abstract
It is proved that ifY ⊂X are metric spaces withY havingn≧2 points then any mapf fromY into a Banach spaceZ can be extended to a map\(\hat f\) fromX intoZ so that\(\left\| {\hat f} \right\|_{lip} \leqq c log n\left\| f \right\|_{lip} \) wherec is an absolute constant. A related result is obtained for the case whereX is assumed to be a finite-dimensional normed space andY is an arbitrary subset ofX.
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Supported in part by US-Israel Binational Science Foundation and by NSF MCS-7903042.
Supported in part by NSF MCS-8102714.
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Johnson, W.B., Lindenstrauss, J. & Schechtman, G. Extensions of lipschitz maps into Banach spaces. Israel J. Math. 54, 129–138 (1986). https://doi.org/10.1007/BF02764938
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DOI: https://doi.org/10.1007/BF02764938