直线与仿射集的关系及距离性分离定理

THE RELATIONS BETWEEN LINES AND AFFINE SETS AND SEPARATION THEOREMS WITH DISTANCE PROPERTY

讨论赋范空间中直线与仿射集的关系。重点讨论平行、不相交且不平行的情形。指出最近平行线的存在性后,建立了带距离性的 Mazur 型分离定理。

In normed linear spaces,the relations between lines and affine sets are discussed.In particular,we study the parallel case and the case neither parallel nor intersecting.It is also considered on their shortest distance and establish some separation theorems of Mazur type with distance property.