We show that a closed piecewise flat 2-dimensional Alexandrov space Σ can be bi-Lipschitz embedded into a Euclidean space such that the embedded image of Σ has a tubular neighborhood in a generalized sense.As an application,we show that for any metric space sufficiently close to Σ in the Gromov-Hausdorff topology,there is a Lipschitz Gromov-Hausdorff approximation.
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