@FabricioOlivetti Thanks for your contributions to the forum!

Could you elaborate with some type of explanation and/or proofs? (As formal or as informal as you like.) To me the most interesting part of the exercises is the concepts that they illustrate. Supplying a proof calls for digging into the concepts. In the best case, such material could lead to further questions, new and different examples, and discussion generally.

The forum is a bit like a fledgling plant with a finicky appetite. We do our best...