Answer to Question #134038 in Real Analysis for Senzo

Question

Let I1, I2 ⊂ R be two bounded open intervals in R. Prove tht

I1 × I2 = { (a, b) : a ∈ I1, b ∈ I2 } ⊂ R2

is an open subset of R2

Answer 1

We know that $I_1$ and $I_2$ are open intervals in $R$, When we multiply two open intervals, we get another interval (subset) that has boundary value from interval $I_1$ and another boundary value from $I_2$. If intervals $I_1$ and $I_2$ are belong to $R_2$ so their product also will belong to $R_2$ . Q.E.D.