Vector space partitions
Given infinite-dimensional real vector spaces $V,W$ with $|W| \leq |V|$, it is shown that there exists a collection of subspaces of $V$ that are isomorphic to $W$, mutually intersect only at 0, and altogether cover $V$.
"Projective partitions of vector spaces",
Electronic Journal of Linear Algebra,
Volume 32, pp. 125-130.