Is a Space Connected if Its Closure Is Connected?

  • Thread starter Thread starter blahblah8724
  • Start date Start date
  • Tags Tags
    closure
blahblah8724
Messages
31
Reaction score
0
If the closure of a space C is connected, is C connected?
 
Physics news on Phys.org
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?
 
blahblah8724 said:
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 _______.
 

Similar threads

I Interior and Closure in a Topological Space .... .... remark by Willard
Replies
2
Views
2K
I Uniform closure of algebra of bounded functions is uniformly closed
Replies
2
Views
2K
I Dyadic cubes generate Borel sigma algebra of subset
Replies
2
Views
995
I Closure & Interior as Dual Notions .... Proving Willard Theorem 3.11 ...
Replies
2
Views
2K
I A problem of completeness of a metric space
Replies
3
Views
2K
I Open balls dense in closed balls in Euclidean space
Replies
2
Views
2K
I Tough lemma on locally finite refinement
Replies
8
Views
2K
MHB Understanding Topology: Closure, Boundary & Open/Closed Sets
Replies
2
Views
2K
A Closure of constant function 1 on the complex set
Replies
11
Views
2K
A Orthogonal complement of the orthogonal complement
Replies
4
Views
4K

Hot Threads

Recent Insights

Back
Top