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Yes. TopologizeFor the first space, topologize$\mathbb R$ by taking the intervals $(-\infty,r)$, $r\in \mathbb R$, for the nonempty proper open subsets for the first space. For the second space, take the subspace with underlying set $\mathbb Q$.
Yes. Topologize$\mathbb R$ by taking the intervals $(-\infty,r)$, $r\in \mathbb R$, for the nonempty proper open subsets for the first space. For the second space, take the subspace with underlying set $\mathbb Q$.
Yes. For the first space, topologize$\mathbb R$ by taking the intervals $(-\infty,r)$, $r\in \mathbb R$, for the nonempty proper open subsets. For the second space, take the subspace with underlying set $\mathbb Q$.
Yes. Topologize $\mathbb R$ by taking the intervals $(-\infty,r)$, $r\in \mathbb R$, for the nonempty proper open subsets for the first space. For the second space, take the subspace with underlying set $\mathbb Q$.
