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 Date: 2004-11-30 18:22:49Linear algebra Functional analysis General topology Mathematical structures Topological vector space Quotient space Vector space Compact space Locally convex topological vector space Topology Algebra Mathematics |
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The purpose of this note is to give a proof of the fact that finite dimensional topological vectorspaces (over a complete normed division ring) have only one possible topology, as well as related facts, such as a locally compact tvs is necessarily finite dimensional. Many of these facts can be found in Paul Garrett’s notes
![A proof of the Markov-Kakutani fixed point theorem via the Hahn-Banach theorem Dirk Werner S. Kakutani, in [2] and [3], provides a proof of the Hahn-Banach theorem](https://www.pdfsearch.io/img/9618aa1838d40558261724bde01db3e4.jpg "A proof of the Markov-Kakutani fixed point theorem via the Hahn-Banach theorem Dirk Werner S. Kakutani, in [2] and [3], provides a proof of the Hahn-Banach theorem")
