Theorems of borsuk-ulam type for flats and common transversals of families of convex compact sets

摘要

Several results on the topology of the space of -flats in similar to the Borsuk-Ulam theorem on coverings of asphere and aball are proved. Some corollaries on common transversals for families of subsets of and on measure partitions by hyperplanes are deduced. Bibliography: 22 titles.