If the closure of a space C is connected, is C connected?
What do you think?? Can you come up with a counterexample?? (this should suggest that the answer is no)
What is the usual way to show that the circle is not homeomorphic to the real line?
Can you think of some dense subsets of the real line?
There's a really easy counterexample. Just take the real line and ______ one single _______.
Separate names with a comma.