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Topic: Open and Shut
Replies: 10   Last Post: Feb 4, 2013 10:50 PM

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William Elliot

Posts: 2,141
Registered: 1/8/12
Re: Open and Shut
Posted: Feb 4, 2013 3:51 AM
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On Sun, 3 Feb 2013, David C. Ullrich wrote:
> William Elliot <marsh@panix.com> wrote:

> >A subset A, of an ordered set is convex when
> >for all x,y in A, for all a, (x <= a <= y implies a in A).
> >
> >I will call an interval an order convex subset of Q.
> >Given an interval, what's the probablity that it's
> > open, closed, both, neither?

> That depends on what initial probability distribution
> you put on the set of intervals.

What probability would you put on them?
Could it be uniform?

> >Given an open subset of Q, what's the probablity that it's clopen?
> >Given an closed subset of Q, what's the probablity that it's clopen?


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