Is a Space Connected if Its Closure Is Connected?

[blahblah8724]

If the closure of a space C is connected, is C connected?

 

[micromass]

What do you think?? Can you come up with a counterexample?? (this should suggest that the answer is no)

 

[Tinyboss]

What is the usual way to show that the circle is not homeomorphic to the real line?

 

[Bacle2]

Can you think of some dense subsets of the real line?

 

[SteveL27]

If the closure of a space C is connected, is C connected?

There's a really easy counterexample. Just take the real line and ______ one single _______.