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Math Help - Sub bases

  1. #1
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    Sub bases

    Can anybody help me with this questions:
    Let (X,T) be T1 space. Show that there is space iff there is a subbase S for T such that:

    x ε H εS implies that there exists a continuous f:x->[0,1] such that f(x) = 1 and f(y) =0 for all y ε X-H
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Turloughmack View Post
    Can anybody help me with this questions:
    Let (X,T) be T1 space. Show that there is space iff there is a subbase S for T such that:

    x ε H εS implies that there exists a continuous f:x->[0,1] such that f(x) = 1 and f(y) =0 for all y ε X-H
    I have yet to see you put any effort forward towards these solutions. Care to give us some work?
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