给出域F上的两个无限维向量空间V、V'，并分别给出n个不同的有限维子空间，在怎样的条件下可以保证存在从V所给出的子空间到V'所给出的子空间的和的同构，保持V、V'所给出的子空间的相互对应。 本文说明了在n=2时若V与V'所给出的子空间保持其任意相互对应的子空间交集的维数相同、在n=3时若V与V'所给出的子空间保持其任意相互对应的子空间交集的维数及所有子空间和的维数相同，可给出所需要的同构。

Let V,V' be infinite dimensional vector spaces over a field F, each with n distinguished finite dimensional subspaces, when does this guarantee the existence of an isomorphism between the sum of the subspaces in V and V' matching corresponding subspaces? The paper shows that the setting where it happens requires that the subspaces have a dimension-preserving correspondence between intersections while n=2;and when n=3, the subspaces should have a dimension-preserving correspondence between both intersections and the total sum.