ultrafilter $\mathcal{F}$

ultrafilter $\mathcal{F}$

I have a question about relation between member of a ultrafilter
$\mathcal{F}$ on a topological space $(X,\tau)$ and a subset $K$ of $X$.
Can we cosider a uniform ultrafilter $\mathcal{F}$ as a partition on $X$?
I mean if $(X,\tau)$ is topological space , $K \subset X$, and
$\mathcal{F}$ is uniform ultrafilter , will have for $ F \in \mathcal{F}$
(1) $F \subset K$ ;
(2) $F ¿ \overline{K} = \emptyset$;
(3) $F ¼ (\overline{K} − K)$.