Interesting. Or put more tersely, Let O be an open set in R^n. There exists a smooth function f: R^n -> R with support cl(O). Off the cuff, I'd try proving th

Interesting. Or put more tersely, Let O be an open set in R^n. There exists a smooth function f: R^n -> R with support cl(O). Off the cuff, I'd try proving this by covering O with bump functions and trying to glue those together. I'll try thinking about this more when I've got time. :)