- #1
jostpuur
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- 19
I know that just because [tex]A\subset X[/tex] and [tex]B\subset X[/tex] are simply connected in some metric space X, the union [tex]A \cup B[/tex] is not neccecarely simply connected. However, the does path connectedness of [tex]A\cap B[/tex] suffice for the union to become simply connected? If it does, is there easy proof?
Edit:
I don't change the original question, because it could make first replies seem strange, but anyway, the question that I'm now interested (after the first replies), is that is the claim true if we assume the intersection to be nonempty, and both A and B to be open.
Edit:
I don't change the original question, because it could make first replies seem strange, but anyway, the question that I'm now interested (after the first replies), is that is the claim true if we assume the intersection to be nonempty, and both A and B to be open.
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