Suppose I have a vector space $K$ which consists of real-valued sequences with only finitely many non-zero terms. I would like to show that there doesn't exist a norm on $K$ that would make it become a complete metric space. My technique is to use the Baire Category Theorem. However, I run into problems because of the generality of the theorem.
Would anyone be kind enough to offer me some tips? thank you!
2026-04-13 14:03:41.1776089021
Proving that there is no norm for the space of real-valued sequences making it a complete metric space.
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