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Topic: Connected?
Replies: 5   Last Post: May 12, 2013 8:52 PM

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William Elliot

Posts: 2,637
Registered: 1/8/12
Re: Connected?
Posted: May 4, 2013 11:30 PM
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On Sat, 4 May 2013, fom wrote:

> On 5/4/2013 8:39 PM, William Elliot wrote:
> > Let S = ([0,1] /\ Q)x[-1,0] \/ ([0,1] /\ R\Q)x[0,1].
> >
> > S appears to be connected but not path connected.
> > Is that correct? How would you proof it?

> I must be reading your notation incorrectly.

> Doesn't this set contain [0,1]x[0] as a line segment?

Oh yes, of course, what was I thinking about?
Sz = ([0,1] /\ Q)x[-1,0] \/ ([0,1] /\ R\Q)x(0,1]?

> If so, wouldn't that facilitate a continuous
> path between any two points consisting of a
> polygonal path with at most three segments?

Indeed it does. I misread the problem.
However, on it's heels, is Sz connected
and not path connected?

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