@LSpice Thanks. Understood. Which means it is still a mystery. My comment was an honest attempt to understand the reaction to the question and I asked you as my best bet for someone who might be involved.

@LSpice Did you downvote the question? Just wondering because while it is not a deep question leading to a long answer it was something that was bugging me and I got a good answer. Did you see anything wrong with the question that it would deserve a downvote?

@Dirk That makes a lot of sense. As you say - the seminorms (based on the supremum) are good for making a topology, and so it is nice to have them there already. Thanks. It gives a motive for the approach.