Discrete Metric Space, The Nature Of The A Crude Embedding,

Yu Guoliang introduces property A of discrete metric spaces which guarantees the coarse embedding into Hilbert space.The relationship between property A and coarse embedding is an attractive problem.A class of metric spaces which can be coarsely embedded into Hilbert space without property A are constructed,which generalizes Nowak's construction in case of non-trivial finite groups to any non-trivial metric space which admits a bi-Lipschitz coarse embedding into/1(e.g,finite metric spaces).