A pair $(X,\tau )$ is called a generalized topological space if $\tau$ is collection of subsets of $X$ so that $\emptyset \in \tau$ and $\tau$ is closed under arbitrary unions. A subset $A$ of GTS $(X,\tau )$ is strongly nowhere dense if for any nonempty open set $U\in \tau$, there exists nonempty open set $V \subset U$ such that $V\cap A=\emptyset$.

A generalized topological space $(X,\tau )$ is called a weak Baire space if there is no nonempty open set $U\in \tau$ such that can be written as a countable union of strongly nowhere dense subsets.

Is there any weak Baire space which is not Baire space?