I need a space with countable tightness which is not Frechet space. In this space, I am searching a poin with no deleted neighborhood entierely of P-poinnts.

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