Relationships Among k-UR, k-NUC, and kR

• Main Authors: Hsu, Chia Yu, 許佳璵
• Other Authors: Ho, Tsing-Jen
• Format: Others
• Language: zh-TW
• Published: 1993
• Online Access: http://ndltd.ncl.edu.tw/handle/55177273709503154488

碩士 === 輔仁大學 === 數學系 === 81 === This thesis will study the relationships among k-UR, k-NUC, and kR for the general closed convex sets in a real Banach space by extending some geometric and topological results which have been established for the closed unit ball. The main results are listed below ：１、Let k.gdsim.1 be an integer. If a bounded closed convex set　　Ｃ with nonempty interior is strictly convex and k-UR with respect to an interior point, then C is (k+1)R.２、Let k.gdsim.2 be an integer. If a closed convex set Ｃ　　with nonempty interior is strictly convex and k-NUC with respect to an interior point, then Ｃ is kR.３、Let k.gdsim.1 be an integer. If a bounded closed convex　　set Ｃ with nonempty interior is k-UR with respect to　 an interior point, then Ｃ is (k+1)-NUC.