How to show the space is Frechet? The space $X$ is monolithic and $t(X)\le \omega$, then How to show $X$ is Frechet? > $X$ is monolithic means that $\operatorname{nw}(\overline{A}) \le \kappa$ for any subset $A$ with the cardinality $\le \kappa$. Thanks for any help.

This is not too hard. Suppose $x$ is in the closure of $A$. Then there is a countable subset $B$ of $A$ such that $x$ is in the closure of $B$ (as $X$ has countable tightness). Now $\overline{B}$ has a countable network (as $X$ is ($\omega$)-monolithic). From this we should maybe get a sequence converging to $x$ from $B$...

**Added** This cannot be salvaged, as the counterexample by Brian shows. It does hold for compact Hausdorff monolithic spaces, as I say in the comments, because then $\overline{B}$ has a countable network and is also compact Hausdorff, and thus is metrizable. So a sequence as stated can then easily be found by first countability. Maybe Paul was working in compact spaces..