| Summary: | 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.
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