Show that the map 3 T : R³→ R² given by ) T(x₁ , x ₂, x₃ ) =(x1,+x2,+x3 is an open map

Word Count : 201

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To show that the linear transformation \( T: \mathbb{R}^3 \to \mathbb{R}^2 \) given by \( T(x_1, x_2, x_3) = (x_1 + x_2 + x_3) \) is an open map, we need to demonstrate that it maps open sets in \( \mathbb{R}^3 \) to open sets in \( \mathbb{R}^2 \).

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Degree : MASTER DEGREE PROGRAMMES
Course Name : M.Sc. Mathematics with Applications in Computer Science
Course Code : MSCMACS
Subject Name : Functional Analysis
Subject Code : MMT 6
Year : 2023