Flat transversals to flats and convex sets of a fixed dimension

• Autores: J. L. Arocha, J. Bracho, L. Montejano
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 213, Nº 2, 2007, págs. 902-918
• Idioma: inglés
• DOI: 10.1016/j.aim.2007.01.017
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• Resumen

  • Helly and Hadwiger type theorems for transversal m-flats to families of flats and, respectively, convex sets of dimension n are proved in the case of general position. The proofs rely on Helly type theorems for ¿linear partitions¿ and ¿convex partitions,¿ so that a general theory of Helly numbers is also developed.