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Let $X_1, \ldots, X_n$ be path connected. Prove that the corresponding product space $X_1 \times \ldots \times X_n$ is path connected.

   Let $X_1, \ldots, X_n$ be path connected. Prove that the corresponding product space $X_1 \times \ldots \times X_n$ is path connected.

Introduction to Topology: Pure and Applied

Introduction to Topology: Pure and Applied

Colin Adams, Robert… 1st Edition

Chapter 6, Problem 52

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A topological space \( Y \) is path connected if for any two points \( y_0, y_1 \in Y \), there exists a continuous map \( f: [0, 1] \to Y \) such that \( f(0) = y_0 \) and \( f(1) = y_1 \). Show more…

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Let $X_1, \ldots, X_n$ be path connected. Prove that the corresponding product space $X_1 \times \ldots \times X_n$ is path connected.

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