Homework Help: Topology proof

1. Feb 18, 2008

pivoxa15

1. The problem statement, all variables and given/known data
Conjecture: If K=a union of subsets of G with K open then each subset in the union is open

3. The attempt at a solution
Can't really see the proof. In fact it's false as any non discrete topology have open sets which are a union of subsets whch may not be open.

Last edited: Feb 18, 2008
2. Feb 18, 2008

morphism

How do you expect to see the proof if you already know that the statement is false?!

3. Feb 18, 2008

quasar987

Or consider the classic example where one takes the reunion of the non-opens sets [1/n,+infty) and get the open sets (0,+infty)

4. Feb 18, 2008

JasonRox

You can practically create a counterexample for any topology except that of the discrete topology.

5. Feb 18, 2008

JasonRox

Why not just take the union of 0 and (-1,1). We get the open set (-1,1) but the point 0 is closed.

6. Feb 18, 2008

pivoxa15

After I created this thread, I realised the conjecture was false.