The unit ball of the Hilbert space in its weak topology

Antonio Avilés

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arXiv · 0903.0154

The unit ball of the Hilbert space in its weak topology

Antonio Avilés

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Abstract

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.

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Antonio Avilés. 2009-03-01. The unit ball of the Hilbert space in its weak topology. https://arxiv.org/abs/0903.0154

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