In this bachelor thesis we present a proof of Kirszbraun's theorem for Hilbert spaces and then we prove a gluing result of Makarychev and Makarychev. Namely we prove that if X = A ∪ B is a metric space such that A embeds into l a 2 with...
moreIn this bachelor thesis we present a proof of Kirszbraun's theorem for Hilbert spaces and then we prove a gluing result of Makarychev and Makarychev. Namely we prove that if X = A ∪ B is a metric space such that A embeds into l a 2 with distortion D A and B into l b 2 with distortion D B , then X embeds into l a+b+1 2 with distortion at most 7D A D B + 5(D A + D B).