Topology Question: Is A Open if Open Subsets of A Union to A?

[JasonJo]

Suppose I have some subset of R, not necessarily an interval, let it be denoted as A. I have some union (might be countable, might be finite, might be uncountable) of sets where each set is an open set of A and the union of the open sets is equal to A. Can I conclude that A is open?

I am not sure because the sets are open in A, not necessarily open in R. I don't know much about A other than it is some subset of R.

Any help?

 

[morphism]

You can't conclude that A is open. For a trivial example, take a non-open subset A of R. Note that A is open in itself.

 

[Dick]

If all that you know is that the sets are open in A this can't tell you anything about whether A is open in R. E.g. A is always open in A.