Product of countably many separable topological spaces

Reference no: EM13990650

1. If Si are sets with discrete topologies, show that the product topology for finitely many such spaces is also discrete.

2. If there are infinitely many discrete Si , each having more than one point, show that their product topology is not discrete.

3. Show that the product of countably many separable topological spaces, with product topology, is separable.

Reference no: EM13990650

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