- #1

latentcorpse

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My problem is in that because the A and B are open and disjoint, when i take the union i keep getting one point omitted which prevents the union from being connected.

i was wondering about [itex]A=\mathbb{Z}[/itex] and [itex]B=\mathbb{R} \backslash \mathbb{Z}[/itex]. These are disjoint, non-empty and open subsets of the real line and when u take their union you get [itex]\mathbb{R}[/itex] which is connected. I'm not sure about the disconnectedness of A and B though...