This question is also posted here.

A space $X$ is callled **semi-stratifiable** space if it has a $g$-function such that: for any point $x$ of $X$ and a sequence $\{x_n\}$ of $X$ if $x \in g(n,x_n)$, then $x_n \to x$.

Note that every Moore space is semi-stratifiable. We know the cardinality of a star countable Moore space is not greater than $\mathfrak c$.

A topological space $X$ is said to be **star countable** if whenever $\mathscr{U}$ is an open cover of $X$, there is a countable subspace $K$ of $X$ such that $X = \operatorname{St}(K,\mathscr{U})$.

Is there a star countable semi-stratifiable space $X$ with $|X|> \mathfrak c$?

Thanks for your help.