Let XZY be a diagram of topological spaces and continuous functions. Describe a topological space A...

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Let XZY be a diagram of topological spaces and continuous functions. Describe a topological space A which has the following two properties: (1) there exist continuous maps ₁: A → X and 7₂: A → Y such that fon₁ = go π₂, and (2) if A', is any other topological space satisfying (1) (so admitting continuous maps π'₁: A' → X and π'½: A' → Y such that fo ₁ = go π₂), then there exists a continuous map A' A such that T₁ = π₁₂ ol. Let XZY be a diagram of topological spaces and continuous functions. Describe a topological space A which has the following two properties: (1) there exist continuous maps ₁: A → X and 7₂: A → Y such that fon₁ = go π₂, and (2) if A', is any other topological space satisfying (1) (so admitting continuous maps π'₁: A' → X and π'½: A' → Y such that fo ₁ = go π₂), then there exists a continuous map A' A such that T₁ = π₁₂ ol.

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ANS WER Let A be the top ological space consisting of all pairs x y such that x X and y Y with th... View the full answer