Show that $\mathbb{Q}$ with the topology induced by the Sorgenfrey line is normal

Asked Jun 18 '16 at 13:41

Active Jun 18 '16 at 13:48

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Show that $\mathbb{Q}$ with the topology induced by the Sorgenfrey line is normal.

Here, the Sorgenfrey line is the line with the topology whose basis are formed as:

$$\{[a,b) : a < b \}$$

I know that, assuming that it is not normal, I have to show that for any two closed sets, every pair of open sets containing each one of them has to be non trivial. How to do this?

edited Jun 18 '16 at 13:48

asked Jun 18 '16 at 13:41

L.F. Cavenaghi

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The answers on this question might be helpful. – Vera Jun 18 '16 at 14:49
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@Leonardo: Specifically, this answer has what you need in a very general form. – Brian M. Scott Jun 18 '16 at 21:53

Show that $\mathbb{Q}$ with the topology induced by the Sorgenfrey line is normal

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