I need a space with countable tightness which is not a Fréchet space. In this space, I am searching for a point with **no** deleted neighborhood consisting entirely of P-points.

(A P-point is a point $x \in X$ such that for every $G_\delta$ set $O$ containing $x$, $x \in \operatorname{int}(O)$ or equivalently $M_x = O_x$, i.e every fixed prime z-filter that contains $x$ is a z-ultrafilter.)