> 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 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?