希尔伯特空间在弱拓扑上的单位球
The unit ball of the Hilbert space in its weak topology
摘要：
证明了希尔伯特空间在其弱拓扑下的单位球是一个离散集的Alexandroff紧化的可数幂的连续象，并推导了当空间不可分时，它的开集格不为其他等价范数的球所共有的一些组合性质.
英文摘要：
We show that the unit ball of a Hilbert space in its weak topology is a continuous image of the countable power of the Alexandroff compactification of a discrete set, and we deduce some combinatorial properties of its lattice of open sets which are not shared by the balls of other equivalent norms when the space is nonseparable.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
