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Math Help - discrete topological space

  1. #1
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    discrete topological space

    Hello friends,

    i need some help with this problem. Any help is welcome

    here is the question

    Show that a topological space X is discrete if and only if all
    subset of X is open

    thank you
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  2. #2
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    Quote Originally Posted by donsmith View Post
    Show that a topological space X is discrete if and only if all subset of X is open
    What is meant by "a topological space X is discrete "?
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  3. #3
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    man my English is horrible , I'm trying to translate the problem

    second try,

    Show that X is a discrete topological space if and only if every subset of X is open
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  4. #4
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    does the question make any sense?
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  5. #5
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    Quote Originally Posted by donsmith View Post
    does the question make any sense?
    The reason I asked for a clarification is that some texts do define a discrete topology with open sets being the power set of the underlying set. If that is it, there is nothing to prove.

    On the other hand, it may be asking you to prove that the power set of a set is in fact a topology on that set.
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