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Math Help - Find a function f: D-> R such that f is continuous but not uniformly continuous

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    Find a function f: D-> R such that f is continuous but not uniformly continuous

    Let p \in[0,1] and D=[0,1]-{p}. find a function f: D->R such that f is continuous at every point of D but is not uniformly continuous on D.

    Would 1/x work for this as well but how do I prove it?
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    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by FernandoRevilla View Post
    yes this is my other post. However i started a new thread with new conditions so it didn't get confusing. At first I thought x^2 would work as well but then based on the other post I thought it would be 1/x but i dont know how to prove it and I didn't think it could be proved the same way as the other post because there are new conditions.
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    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by alice8675309 View Post
    yes this is my other post. However i started a new thread with new conditions so it didn't get confusing. At first I thought x^2 would work as well but then based on the other post I thought it would be 1/x but i dont know how to prove it and I didn't think it could be proved the same way as the other post because there are new conditions.

    You only need to choose p = 0 .
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