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Math Help - showing that a topological space is t4

  1. #1
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    showing that a topological space is t4

    Hi there

    If I can prove that any point in a topology is open (for example the Sorgenfrey line) then it logically follows that the topological space concerned is T4 am I right?

    Are there other usual ways to show whether a topological space is T4?

    Regards
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  2. #2
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    Re: showing that a topological space is t4

    It doesn't make sense to say that "any point in a topology is open". "Open" is a property of sets of points, not individual points. Did you mean to say that "singleton sets", sets containing a single point?
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  3. #3
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    Re: showing that a topological space is t4

    Yes singleton sets are meant, sorry.

    Does anyone know how to show that a topological space (for instance the Sorgenfrey line) is T4 ? What does one have to show to conclude T4?

    Regards
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  4. #4
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    Re: showing that a topological space is t4

    If singleton sets are open, then all sets are both open and closed. I.e., we have the"discrete" topology on the set. And it is trivially true that such a space is T4.
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