Closure and connected spaces

1. Feb 29, 2012

blahblah8724

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

2. Feb 29, 2012

micromass

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

3. Feb 29, 2012

Tinyboss

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

4. Feb 29, 2012

Bacle2

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

5. Feb 29, 2012

SteveL27

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