Exercise 5. Let n = N and for each 1 ≤ i ≤ n let (Xi, Ti) be a topological space. Prove that the product space X₁ × ... × X is a Hausdorff space (with respect to the product topology) if and only if (Xi, Ti) is a Hausdorff space for all 1 ≤ i ≤ n.

Exercise 5. Let n = N and for each 1 ≤ i ≤ n let (Xi, Ti) be a topological space. Prove that the product space X₁ × ... × X is a Hausdorff space (with respect to the product topology) if and only if (Xi, Ti) is a Hausdorff space for all 1 ≤ i ≤ n.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.2: Vector Spaces

Problem 38E: Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1)...

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Exercise 5. Let n = N and for each 1 ≤ i ≤ n let (Xi, Ti) be a topological space. Prove that
the product space X₁ × ... × X is a Hausdorff space (with respect to the product topology)
if and only if (Xi, Ti) is a Hausdorff space for all 1 ≤ i ≤ n.

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