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In this paper, we introduce the concept of uniformly bounded fibred coarseembeddability of metric spaces, generalizing the notion of fibred coarseembeddability defined by X. Chen, Q. Wang and G. Yu. Moreover, we show itsrelationship with uniformly bounded a-T-menability of groups. Finally, we givesome examples to illustrate the differences between uniformly bounded fibredcoarse embeddability and fibred coarse embeddability.

Uniformly bounded fibred coarse embeddability and uniformly bounded a-T-menability