摘要： Let (xn) be a sequence in Rk. The Schauder equivalence relation E (Rk,( xn )) on RN defined as: for a,b ∈ RN, (a,b) ∈ E (Rk,( xn )) iff Σn
(a (n) - b(n) ) xn converges. For 1 ≤ t ≤ k, denote cs(t ) be the set of all a ∈ RN with Σm a (mt + j ) converges for each j = 0,1,?,t - 1. It's proved that, if ( xn ) ≠ 0 for infinitely many n, then E (Rk,( xn )) ～ B RN /cs(t ) for some t ≤ k.