Theorems of Borsuk-Ulam type for flats and common transversals

Details Theorems of Borsuk-Ulam type for flats and common transversals Theorems of Borsuk-Ulam type for flats and common transversals

2009-05-17

arxiv.org/abs/0905.2747v3

Math. Sbornik, 200:10, 2009, 39-58

Mathematics

Combinatorics

Corrected typos and added the journal reference

Scientific paper

10.1070/SM2009v200n10ABEH004045

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 of
sphere. 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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