众所周知任何K空间X必代数且格同构于K空间C_∞(Q)的某完备正规子空间,其中Q是極端重紧致,C_∞(Q)表示Q上除一稀疏集外取值有限的实连续函数全体.曾提出问题:关于K_σ空间有否类似的结果?作者得到下面的定理说明了在较弱的形式下,此问题的答案是肯定的. 定理:任何K_σ空间X必代数且格同构于K_σ空间C_∞(Q)的某完备子空间,其中Q It is well known that any K-space X must be algebraic and isomorphic to a perfect normal subspace of the K-space C_∞ (Q), where Q is extremely compact and C_∞ (Q) means that the value of Q except for a sparse set is finite The question has been answered: Is there any similar result with respect to K_σ space? The author obtains the following theorem which shows that in the weaker form, the answer to this question is affirmative. Theorem: Any K_σ space X must be algebraic and Lattice isomorphic in some complete subspace of C_∞ (Q) in K_σ space, where Q