Let p : ℝ2 → ℝ be the function defined by p(x, y) = x. Which of the following statements are true?
1
Let A1 = {(x, y) ∈ ℝ2 | x2 + y2 < 1}. Then for each γ ∈ p(A1), there exists a positive real number ε such that (γ - ε, γ + ε) ⊆ p(A1).
2
Let A2 = {(x, y) ∈ ℝ2 | x2 + y2 ≤ 1}. Then for each γ ∈ p(A2), there exists a positive real number ε such that (γ - ε, γ + ε) ⊆ p(A2).
3
Let A3 ={(x, y) ∈ ℝ2 | xy = 0}. Then for each γ ∈ p(A3), there exists a positive real number ε such that (γ - ε, γ + ε) ⊆ p(A3).
4
Let A4 = {(x, y) ∈ ℝ2 | xy = 1}. Then for each γ ∈ p(A4), there exists a positive real number ε such that (γ - ε, γ + ε) ⊆ p(A4).