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Thread: epislon chain problem

  1. #1
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    epislon chain problem

    Please help with this problem, Im stuck.


    metric space (M,d)

    Prove:

    Given p $\displaystyle \in $ M, the set of points q such that there exists a $\displaystyle \epsilon $-chain joining p and q is both open and closed in M. Conclude that in a connected metric space, any two points can be $\displaystyle \epsilon $-chained to each other.
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  2. #2
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    Quote Originally Posted by ElieWiesel View Post
    metric space (M,d)
    Prove:
    Given p $\displaystyle \in $ M, the set of points q such that there exists a $\displaystyle \epsilon $-chain joining p and q is both open and closed in M. Conclude that in a connected metric space, any two points can be $\displaystyle \epsilon $-chained to each other.
    I think that you need to define $\displaystyle \epsilon-\text{chained} $.
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