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Math Help - If no proper subset of X is dense..

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    If no proper subset of X is dense..

    If no proper subset of the topological space X is dense, is the topology necessarily discreate?
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  2. #2
    Super Member girdav's Avatar
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    Re: If no proper subset of X is dense..

    Take x\in X and let A:=\complement\{x\}. A is not dense, and \overline{A}=\overline{\complement\{x\}}=\overset{  \circ}{\{x\}}^c hence \overset{\circ}{\{x\}}\neq \emptyset and \{x\} is open.
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