# Uncountable sets and isolated points

Given the standard topology, is there any relationship between dense, uncountable sets and isolated points? For example, the set of irrationals is both dense and uncountable and contains no isolated points.

Just something I've been wondering working my way through real analysis.

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is there a restricted context to this question? eg, are we just talking about $\mathbb{R}^n$? – Dustan Levenstein Mar 22 '12 at 20:08
Just $\mathbb{R}$, $n=1$ – docjay Mar 22 '12 at 20:10