9.8. Finite Products

How do we create new topological spaces from old ones?

• Subspaces

• Quotient spaces

• product spaces

9.8.1. The product topology

Given topological spaces \((X_1, \mathcal{T}_1), (X_2, \mathcal{T}_2), \dots, (X_n, \mathcal{T}_n)\) how do we define a reasonable topology \(\mathcal{T}\) on the product set \(X_1 \times X_2 \times \dots \times X_n\)?