【摘要】 对维数不小于3的实赋范线性空间中任给的单位向量x和任给的不超过1的非负实数γ,证明了等腰正交于x且含于半径为γ的球面的向量构成的集合是道路连通的.利用这一结果证明了平分集径向投影的道路连通性,也证明了对3维实赋范线性空间中的任一单位向量均存在含该向量的两两等腰正交的单位向量基.更多还原

【Abstract】 It is proved that,for an arbitrary unit vector x in a normed linear space whose dimension is not less than 3 and each non-negative number γ not greater than 1,the set of vectors isosceles orthogonal to x contained in the sphere whose radius is γ is path-connected. Using this result,the path-connectivity of radial projection of bisectors is proved. It is shown that for an arbitrary unit vector in a 3-dimensional normed linear space,there exists a normal base containing this vector whose elements are pairwise isosceles orthogonal.更多还原