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Where can I read about the Stone-Cech compactification of the separable Hilbert space?

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    What do you want to know about it?2012-07-13
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    When will you accept the answers to your other questions?2012-07-13
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    @NateEldredge, Maybe a concrete example of a space that is isomorphic to the Stone-Cech compactification of the separable Hilbert space. But in general every information on this topic...2012-07-13
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    "Every information on this topic" - does this strike you as a *reasonable* request?2012-07-13
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    Also, what counts as a concrete description? Have you thought about the Stone-Cech compactification of the real line?2012-07-13

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Hilbert space $l^2$ is homeomorphic to product space $\mathbb R^\infty$, but Stone-Cech compactification of that space is not very nice either. Probably the best thing is to read about the Stone-Cech compactification in general. Check (haha) your library for The Stone-Cech Compactification by Russel Walker.