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

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Registered: 1/6/11
Re: Uncountable?
Posted: Apr 25, 2014 3:12 AM
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In article <Pine.NEB.4.64.1404250003140.11979@panix2.panix.com>,
William Elliot <marsh@panix.com> 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.

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