拓扑线性空间上连续线性泛函的延拓

本文在线性空间中给出了线性球的定义，由此我们得出：拓朴线性空间中连续线性泛函延拓定理成立的主要条件为当其任意子空间中的线性球为开集时，存在原拓扑上的凸邻域，使此凸邻域限制在子空间上时属于线性球。

The Extension of Continuous Linear Functions

This paper defines the linear sphere in linear spaces and thereby obtains the necessary and sufficient condition for the extension theorem of a continuous linear function to be right in the topological vector space. In other words, when a linear sphere in a subspace is open there is a convex neighbourhood in the topological vextor space such that it is a subset of the linear sphere in the subspace.