Behaviour of positive function on compact sets Let $v$ be any strictly positive bounded function on $\Omega \subset \mathbb{R}^n$ and zero on $\partial \Omega.$ 
Can we say that for each compact subsets (w.r.t usual topology defined on $\mathbb{R}^n $) of $\Omega$ there exists a constant $c$ such that $v \geq c >0$?
If not, what can be the example?

Well let x(n)=p+ (1\n)p  with p in the compact set (say a say a closed ball about p lying in your open set and n sufficiently large. Let v(x(n)) =1/n with . v(q)=1 at other points in your open set ( and 0 on the boundary ).   
