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 - Topological vector space - Document - PDFSEARCH.IO

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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 Add to Reading List Document Date: 2004-11-30 18:22:49 Open Document File Size: 63,97 KB Share Result on Facebook Person Paul Garrett / / SocialTag Linear algebra Functional analysis General topology Mathematical structures Topological vector space Quotient space Vector space Compact space Locally convex topological vector space Topology