Finding basis which is non stable under finite intersection
Yes, there are counterexamples. Consider, for instance, the basis of open balls in $\mathbb{R}^2$. The intersection of two balls is, in general, not a ball anymore.
Finding basis which is non stable under finite intersection
Yes, there are counterexamples. Consider, for instance, the basis of open balls in $\mathbb{R}^2$. The intersection of two balls is, in general, not a ball anymore.