In this paper some results on the topology of the space of $k$-flats in$\mathbb R^n$ are proved, similar to the Borsuk-Ulam theorem on coverings ofsphere. Some corollaries on common transversals for families of compact sets in$\mathbb R^n$, and on measure partitions by hyperplanes, are deduced.
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机译：本文证明了关于$ \ mathbb R ^ n $中$ k $ -flats空间拓扑的一些结果，类似于关于球形覆盖的Borsuk-Ulam定理。推导了关于\ mathbb R ^ n $中的紧集族的常见横截面以及通过超平面测度划分的一些推论。
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