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Topic: Uncountable?
Replies: 9   Last Post: Apr 26, 2014 2:13 PM

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Virgil

Posts: 9,012
Registered: 1/6/11
Re: Uncountable?
Posted: Apr 25, 2014 1:52 PM
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In article <ad3kl9tum3fm2lb8f9fehagjb4fumm7h3a@4ax.com>,
quasi <quasi@null.set> wrote:

> Virgil wrote:
> >William Elliot wrote:
> >

> >>Let C be a collection of open subsets of R that cover Q.
> >>Can S = R - \/C ever be uncountable?

> >
> >It cannot even be non-empty!
> >
> >Every open cover of Q as a subset of R covers R.

>
> That's not true.
>
> As a simple example, let
>
> A = (-oo,sqrt(2))
>
> B = (sqrt(2),oo)o]


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