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Christian Remling
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Can you write R^2$\mathbb R^2$ as a disjoint union of two totally disconnected sets?

Can you write R^2$\mathbb R^2$ as a disjoint union of two totally disconnected sets?

Can you write R^2 as a disjoint union of two totally disconnected sets?

Can you write R^2 as a disjoint union of two totally disconnected sets?

Can you write $\mathbb R^2$ as a disjoint union of two totally disconnected sets?

Can you write $\mathbb R^2$ as a disjoint union of two totally disconnected sets?

Post Reopened by Benjamin Steinberg, Joonas Ilmavirta, Jeremy Rickard, Emil Jeřábek, Bjørn Kjos-Hanssen
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Nima
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Can you write R^2 as a disjoint union of two totally disconnected sets?

Can you write R^2 as a disjoint union of two totally disconnected sets?