本文指出了赋范线性空间上的一些局部凸拓扑的完备性与它的单位球上相应的诱导拓扑的完备性之间的关系。

The relation between the completeness of several local convex topology in normed vector space and that of induction topology of its unit ball was pointed out in this paper.

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研究了Cartan域上的极值问题。建立Cartan域的单位球之间极值问题的一个定理并给出它的一个应用。

We revisit the classical extremal problem on Cartan domains. We first establish theorems for the extremal problem between Cartan domain and the unit ball.

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