On L1-Embeddability of Unions of L1-Embeddable Metric Spaces and of Twisted Unions of Hypercubes

On L1-Embeddability of Unions of L1-Embeddable Metric Spaces and of Twisted Unions of Hypercubes

Blog Article

We study properties of twisted unions of metric spaces introduced in [Johnson, Lindenstrauss, and Schechtman 1986], and in [Naor Generator Wire and Rabani 2017].In particular, we prove that under certain natural mild assumptions twisted unions of L1-embeddable metric spaces also embed in L1 Collections with distortions bounded above by constants that do not depend on the metric spaces themselves, or on their size, but only on certain general parameters.This answers a question stated in [Naor 2015] and in [Naor and Rabani 2017].