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Math Help - [Topology] Connected Spaces

  1. #1
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    [Topology] Connected Spaces

    I realy need some help in the following questions:

    1. Let X be a topological space and let A be subgroup of X that contains one and only point from each connected component of X. Prove that X/A is connected.

    2. Let X=R-{0} be a subspace of R. Prove that for each n=1,2,3,4... - X^n is locally connected but X^N is not locally connected...


    Thanks a lot !
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by WannaBe View Post
    I realy need some help in the following questions:

    1. Let X be a topological space and let A be subgroup of X that contains one and only point from each connected component of X. Prove that X/A is connected.

    2. Let X=R-{0} be a subspace of R. Prove that for each n=1,2,3,4... - X^n is locally connected but X^N is not locally connected...


    Thanks a lot !
    What have you done? For one, did you mean subspace or actually subgroup?
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  3. #3
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    I meant subspace ofcourse... Sry for the mistake...
    I actually have no idea how to start thinking of these two questions... I hope you will be able to give me some hints that will give me a small push here...

    Thanks
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