GATE 2025 MA – Question 46

Topology · Topological Spaces and Constructions · 2 marks · Multiple choice

X=ℝ and Y=[0,1], each with the usual distance. In which space is [0,1/4) open?

Show answer and explanation

Correct answer: (B) Y but not X

Explanation

In Y the interval equals Y∩(−1,1/4), hence is relatively open. In ℝ, every open ball around 0 includes negative points, so it is not open. **B**.

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