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Math Help - i need the proof fpr this statement

  1. #1
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    i need the proof fpr this statement

    hello;
    please Ineed the poof of this statement:
    "If X is acluster point of A subset of R and U any open set ofX can have no isolated points"
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  2. #2
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    Quote Originally Posted by raed View Post
    hello;
    please Ineed the poof of this statement:
    "If X is acluster point of A subset of R and U any open set ofX can have no isolated points"
    Please read that statement.
    What does it say? Is something left out?
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  3. #3
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    Quote Originally Posted by raed View Post
    hello;
    please Ineed the poof of this statement:
    "If X is acluster point of A subset of R and U any open set ofX can have no isolated points"


    I'm afraid your question makes no sense: try to write it down again carefully.

    Tonio
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  4. #4
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    Quote Originally Posted by tonio View Post
    I'm afraid your question makes no sense: try to write it down again carefully.

    Tonio
    Let x be a space having no isolated points .prove that every open subset of x can have no isolated points
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  5. #5
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    Quote Originally Posted by raed View Post
    Let x be a space having no isolated points .prove that every open subset of x can have no isolated points

    Well this is trivial, unless I'm missing something or the question's missing something: if some open subset A of X has an isolated point then that point is an isolated ppoint of X...

    Tonio
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  6. #6
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    Quote Originally Posted by tonio View Post
    Well this is trivial, unless I'm missing something or the question's missing something: if some open subset A of X has an isolated point then that point is an isolated ppoint of X...

    Tonio
    yes
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