19.7.1 Properties of sets

Problem: In the three-dimensional space \( \mathbb{R}^{3} \) with standard metric, let's consider the set \( A=\mathbb{Q} \times \mathcal{T} \times \mathbb{R} \) and the point \( x_{0}=(1 ; \sqrt{2} ; 0) \). Which of the following statements are correct: 1) \( x_{0} \) is an interior point of the set \( A \), 2) \( x_{0} \) is the adherent point of the set \( A \), 3) \( x_{0} \) is a limit point of the set \( A \), 4) \( x_{0} \) is an isolated point of the set \( A \), 5) \( x_{0} \) is a boundary point of the set \( A \).