# Moscow space-Examples

A space $X$ is called $Moscow$, if for each open subset $U$ of $X$, the closure of $U$ in $X$ is the union of a family of $G‎_{δ}$‎‎‎ ‎-subsets of $X$ .

For example, Every first countable $T_1$ space is a moscow space.

If $X$ is Hausdorff and either perfectly $\kappa$-normal, of countable pseudocharacter, or extremally disconnected, then $X$ is a Moscow space; all of these are clear from the definitions. There’s a theorem that an arbitrary product of first countable spaces is a Moscow space, but I’ve not seen a proof of it. – Brian M. Scott Jan 28 '13 at 6:30
@BrianM.Scott First, thank you for the advice. I can show that every Extremally disconnected and every perfectly $\kappa$-normal space is a moscow space by definitions, But i can not comprehend the definition of "space of countable pseudocharacter". Is it true that a space $X$ of countable pseudocharacter means every point of the space $X$ is an intersection of countably many of its neighbourhoods? – M.Sina Jan 29 '13 at 17:33
Yes: or as I would put it, every singleton is a $G_\delta$-set. Thus, every set in the space is a union of $G_\delta$-sets. – Brian M. Scott Jan 29 '13 at 18:43