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

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?

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

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.