The Lang-Plaut problem asks whether every subset of a Hilbert space that is a doubling metric space admits a representation in some finite-dimensional Euclidean space with finite metric embedding distortion. Both the dimension and the distortion may depend on the subset.
Lang-Plaut Problem
See also
Banach Space, Dimension Reduction, Doubling Metric Space, Hilbert Space, Metric Embedding DistortionExplore with Wolfram|Alpha
References
Gottlieb, L.-A. and Krauthgamer, R. "A Nonlinear Approach to Dimension Reduction." Disc. Comput. Geom. 54, 291-315, 2015. https://doi.org/10.1007/s00454-015-9707-9.Cite this as:
Weisstein, Eric W. "Lang-Plaut Problem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Lang-PlautProblem.html