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In a paper, the author says that if there exists a $Q$-set, then there exists a "normal" Mrowka space. But the details in the paper is few, and I cannot understand.

I want to know how to prove the space is normal. Could somebody help me?

A subset $A$ of real line is called a $Q$-set if every subset of $A$ ia a $G_\delta$-set in $A$.

Thanks for your help.

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    Where in this paper? $Q$ set does not appear in it. – 2017-01-21
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    $Q$-sets are usually combined in Michael line spaces (see the same topology blog for more info on those) – 2017-01-21
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    @HennoBrandsma $Q$-set and Mrowka space appear between Proposition 1.2 and lemma 1.3. – 2017-01-22
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    These aren't proved in this paper, they refer to older papers (without the quotation to back it up), I believe. The existence might have been proved in the book Consequences of Martin's Axiom by Fremlin. There is some stuff on $Q$-sets in there and on Mrowka spaces. It's classical stuff, "folklore" as it were. – 2017-01-22
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    It's not in Fremlin's book. I checked. I found several papers mentioning normality of $\Psi$-spaces, none of them matching this result. – 2017-01-22
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    In the section on $Q$-sets in http://www.auburn.edu/~gruengf/7550/7550.14pfs.pdf one can get ideas, as think. – 2017-01-22
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    @HennoBrandsma Thanks for the link. It is very helpful for me! – 2017-01-27

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