# need an example here

• Nov 25th 2011, 04:58 PM
wopashui
need an example here
Let A and B be closed subsets of M, and supposed that both $\displaystyle A \bigcup B$ and $\displaystyle A \bigcap B$ are connected. Prove that A and B are connected.

Find an example of disconnected subsets A,B of R such that $\displaystyle A \bigcup B$and $\displaystyle A \bigcap B$ are connected.
• Nov 25th 2011, 07:58 PM
Drexel28
Re: need an example here
Quote:

Originally Posted by wopashui
Let A and B be closed subsets of M, and supposed that both $\displaystyle A \bigcup B$ and $\displaystyle A \bigcap B$ are connected. Prove that A and B are connected.

Find an example of disconnected subsets A,B of R such that $\displaystyle A \bigcup B$and $\displaystyle A \bigcap B$ are connected.

Ok, I helped you with the other two. What are your ideas for this one?
• Nov 28th 2011, 12:39 PM
wopashui
Re: need an example here
Quote:

Originally Posted by Drexel28
Ok, I helped you with the other two. What are your ideas for this one?

sorry, I have proved the statement, but i'm stuck with the example part, need help on it
• Nov 28th 2011, 01:34 PM
Plato
Re: need an example here
Quote:

Originally Posted by wopashui
sorry, I have proved the statement, but i'm stuck with the example part, need help on it

$\displaystyle \begin{gathered} A = (1,2) \cup (3,4) \hfill \\ B = (0,3] \cup [4,6] \hfill \\ \end{gathered}$
• Nov 28th 2011, 08:23 PM
wopashui
Re: need an example here
Quote:

Originally Posted by Plato
$\displaystyle \begin{gathered} A = (1,2) \cup (3,4) \hfill \\ B = (0,3] \cup [4,6] \hfill \\ \end{gathered}$

thanks, in this example, AUB= (0,6) which is connected, and A intersect B= empty set which is connected, and A is disconnected. But is B disconnected? what is the disconnection might be?
• Nov 29th 2011, 03:23 AM
Plato
Re: need an example here
Quote:

Originally Posted by wopashui
thanks, in this example, AUB= (1,7) which is connected, and A intersect B= empty set which is connected, and A is disconnected. But is B disconnected? what is the disconnection might be?

ok