# showing that a topological space is t4

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• Jan 23rd 2013, 11:57 PM
huberscher
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
• Jan 26th 2013, 07:57 PM
HallsofIvy
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?
• Feb 2nd 2013, 07:17 AM
huberscher
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
• Feb 3rd 2013, 05:33 PM
HallsofIvy
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.