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

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fom

Posts: 1,969
Registered: 12/4/12
Re: Connected?
Posted: May 4, 2013 11:06 PM
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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?

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





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