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Topic: countable set of closed subspaces in separable Hilbert space question
Replies: 14   Last Post: Nov 13, 2012 10:29 PM

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William Elliot

Posts: 1,226
Registered: 1/8/12
countable union of closed sets
Posted: Nov 13, 2012 10:29 PM
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On Sun, 11 Nov 2012, Daniel J. Greenhoe wrote:

> I have noted that the "countable union of closed sets" is called F_sigma
> in the literature while G_delta is the "countable intersection of open
> sets":


> Would there be some connection or fundamental result involving F_sigma
> sets? Could the Baire Category Theorem be useful here?


Yes, every open subset of a metric space is F_sigma.
No, that doesn't need the Baire Category Theorem.




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