半范的Gteaux可微性和半范空间的完备性

G■teaux differentiability of seminorm and completeness of seminorm space

在局部凸空间上考虑半范的性质,得到了半范的G teaux可微等价条件,并在由局部凸空间上的所有半范构成的集合上赋予一个完备的度量,且证明了等价半范集在此度量空间中的开性.

The author proves an equal condition to the Gteaux differentiability of seminorm in locally convex space and define a metric in the seminorm space which is complete and the seminorms equal to each other compose a open set in this complete space.