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\begin{remark}
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\begin{remark}
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\begin{itemize}
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\begin{itemize}
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\item If $\emptyset \neq O \R$
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\item If $\emptyset \neq O \overset{\text{open}}{\subseteq} \R$
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then $O \sim \R$.
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then $O \sim \R$.
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\item If $O \subseteq \R$
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\item If $O \subseteq \R$
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is open, then $O$ is the union of open intervals
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is open, then $O$ is the union of open intervals
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