# Stone-Cech compactification of the separable Hilbert space

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? –  Nate Eldredge Jul 13 '12 at 15:47
When will you accept the answers to your other questions? –  draks ... Jul 13 '12 at 16:58
@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... –  user25640 Jul 13 '12 at 17:20
"Every information on this topic" - does this strike you as a reasonable request? –  user16299 Jul 13 '12 at 18:51
Also, what counts as a concrete description? Have you thought about the Stone-Cech compactification of the real line? –  user16299 Jul 13 '12 at 18:52

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.