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Results tagged with locally-convex-spaces
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user 131781
Topological vector space with a locally convex topology, i.e. induced by a system of seminorms.
7
votes
Accepted
Are linear continuous mappings open on totally bounded sets?
Bounded sets, e.g., unit balls in normed spaces, are always totally bounded for weak topologies. So you only have to find such a ball with two incompatible weak topologies, which is easy to do—say the …
- 2,472
2
votes
On Köthe sequence spaces
This is an addendum to the information that you already have. Firstly, there are three sources of substantial results on Köthe spaces—unsurprisingly the first volume of his monograph (which also has …
- 2,472
5
votes
Accepted
Compatibility of inductive and projective limits with dualization in functional analysis
Here are some remarks on the inductive limit case:
The dual of the inductive limit is ALWAYS identifiable (as a vector space) with the projective limit of the duals. This is just the universal proper …
- 2,472
3
votes
$L^{\infty}$ as colimit
When I read your question, I assumed that you were asking whether there is a way to do this in the context of the underlying structure rather in the spirit of the answer above which addresses the situ …
- 2,472