Incoherent systems and coverings in finite dimensional Banach spaces (Q2921151)

The covering problems in Banach spaces have been widely investigated by several authors (J. Connett, L. Cheng, J. M. F. Castillo, V. Fonf and C. Zanco) in geometry. In this work, the author contributes to this topic with some nice results. He investigates the construction of the coverings of the unit ball of a finite dimensional Banach space. This problem is related to the famous Borsuk's conjecture as well. Using the classical results of this topic and studying the incoherent systems, the author develops a new algorithm to construct good coverings. First, he builds a good covering using balls with radius close to one, and then he iterates this construction to get a good covering for any radius.NEWLINENEWLINEFinally, the author analyses and demonstrates the power of the above constructions using some specific examples.