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Q90Section C (Part C)90 of 120

Topology of Q+Q2\mathbb Q+\mathbb Q\sqrt2 inside R\mathbb R

Consider R\mathbb R with the usual topology and S={a+b2∣a,b∈Q}⊂RS=\{a+b\sqrt2\mid a,b\in\mathbb Q\}\subset\mathbb R with the subspace topology. Which of the following statements are true?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Options

Select every correct option, then submit.