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Math Help - Simplest counterexample about path connectedness

  1. #1
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    Simplest counterexample about path connectedness

    We know that path connectedness implies connectedness, but the converse doesn't hold.

    What's the simplest counterexample?
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  2. #2
    Senior Member roninpro's Avatar
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    I've seem comb space most frequently.

    Comb space - Wikipedia, the free encyclopedia
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Connected View Post
    We know that path connectedness implies connectedness, but the converse doesn't hold.

    What's the simplest counterexample?
    Or the Topologist sign curve.
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