Let f: D->R be continuous at a point a$\displaystyle \in$D and assume f(a)>0. How would I prove that there exists a $\displaystyle \delta$>0 such that f(x)>0 for all x$\displaystyle \in$D$\displaystyle \cup$(a-$\displaystyle \delta$, a+$\displaystyle \delta$)?