EDB — 0GS

Exercises

1. [0GS]Note:Written exam of 25 March 2017.Let \((X, τ )\), \((Y , θ) \) be two topological spaces with non-empty intersection and assume that the topologies restricted to \(C=X ∩ Y\) coincide (i.e. \(τ_{| C} = θ_{| C} \))  ¹ and that \(C\) is open in both topologies (i.e. \(C∈ τ, C∈ θ\)). Prove that there is only one topology \(σ\) on \(Z=X ∪ Y\) such that \(σ_{| X} = τ\) and \(σ_{|Y} = θ\) and that \(X,Y∈ σ\).

   Solution 1

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