$\newcommand{\bd}{\operatorname{bd}}$Prove that the $\bd(\bd(\bd(W)))=\bd(\bd(W))$ where $W$ is a subset of the topological space $(X,\mathscr{T})$.
How do you prove that $\mathsf{bd}(\mathsf{bd}(\mathsf{bd}(W)))= \mathsf{bd}(\mathsf{bd}(W))$
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general-topology
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2Is $\mathsf{bd}$ the boundary? – 2011-10-25
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0@Rasmus: no. For example, consider $\mathbb{Q}$ in the ambient space $\mathbb{R}$. Then $\operatorname{bd}(\operatorname{bd}(\mathbb{Q}))=\operatorname{bd}(\mathbb{R})={\varnothing}$. – 2011-10-25