On Wikipedia, it is claimed that the finite sequences space $\mathbb{K}^\infty$ with the final topology is a locally convex topological vector space. But I couldn't figure out how to prove this, both for why it is a topological vector space and why it is locally convex. Can someone help me with this? Thanks a lot.
2026-03-28 02:23:48.1774664628
Why the finite sequences space $\mathbb{K}^\infty$ with the final topology is a locally convex topological vector space?
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