# What is meaning of $\omega$-dense

As the title explains, I want to know what is meaning of some subset is $\omega$-dense in the some whole space?

In Proposition 1.27 of that same paper it states, "If $Y$ is $\omega$-dense in $X$ in the sense that $X = \bigcup \{ \overline{B} : B \in [ Y ]^{\leq \omega} \}$..." so it appears that $Y$ is $\omega$-dense in $X$ if every point of $X$ is in the closure of some countable subset of $Y$. –  Arthur Fischer Feb 8 '13 at 4:51