Open Subsets of a Union: A Conjecture

[pivoxa15]

Homework Statement

Conjecture: If K=a union of subsets of G with K open then each subset in the union is open

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.

 

[morphism]

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

 

[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)

 

[JasonRox]

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

 

[JasonRox]

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)

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

 

[pivoxa15]

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

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