# 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?

Thanks ahead:)

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I suspect that it means countable and dense, but I've never seen that precise term before. –  Cameron Buie Feb 8 '13 at 3:17
Where did you see this term? –  Arthur Fischer Feb 8 '13 at 4:05
In the theorem 1.29 of the paper: On the extent of star countable spaces by the Ofelia T. Alas and others. The paper you can get by google. –  Paul Feb 8 '13 at 4:42
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
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