It is shown in the first part of theorem 2, or the main results, that under GCH the Hilbert spaces over the same number field will be isomorphic if they have the same cardinal number α ( α is a limit ordinal number). 其中定理2之1°是主要结果,它表明:在GCH之下,如果同数域上的Hilbert空间的Hamel维数同为a(a为极限序数)则同构。