Closure of S may be connected without S being connected
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Closure of S may be connected without S being connected

[From: ] [author: ] [Date: 11-11-02] [Hit: ]
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Prove or disprove

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The answer is yes but it's not a general theorem since there are many connected topological spaces. If you want an example consider R\x-axis is not connect but it's closure, which is R, is connected.
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