/closure of A/

In is open? /topological space/

Thank you in advance!

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- March 1st 2011, 12:22 PMzadirInterior, closure, open set in topological space

/closure of A/

In is open? /topological space/

Thank you in advance! - March 1st 2011, 12:57 PMgirdav
You can show that if you have two topological spaces and and if you consider the product space you will have for any and that and .

- March 2nd 2011, 12:44 PMzadir
- March 2nd 2011, 06:46 PMDrexel28
He's saying that if you consider giving the usual topology induced by the usual norm then the induced topology is the same as if the product topology (when both copies of the reals are endowed with the usual topology). That said, for the product topology it's easy to prove things like . So now since are both dense in you can conclude that is dense in . etc.