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Results tagged with locally-convex-spaces
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user 7410
Topological vector space with a locally convex topology, i.e. induced by a system of seminorms.
16
votes
Accepted
Why is multiplication on the space of smooth functions with compact support continuous?
You can spare yourself the functional analytic abstract nonsense by using an explicit set of seminorms on $\mathcal{D}(\mathbb{R}^d)=C_{c}^{\infty}(\mathbb{R}^d)$
which, unfortunately, are not well-kn …
4
votes
Accepted
Known dense subset of Schwartz-like space and $C_c^{\infty}$?
I don't know about "well known" or canonical answers to this question, but it is easy to construct an $X$ that works as follows.
Using the definition of Hermite polynomials given by
$$
H_n(x)=(-1)^n e …
1
vote
Weak convergence of probability measures on weak versus strong dual
Just after posting this MO answer Generalization of Lévy's continuity theorem for nuclear spaces I went and looked again at Fernique's remarkable article and he answered my question above in the affir …
1
vote
On Köthe sequence spaces
Good question. I think these sequence spaces deserve to be better known because they provide a rich bank of concrete examples for things related to the theory of topological vector spaces which can be …
1
vote
Topologies on space of compactly supported continuous functions
A bit long for a comment so I will post it as an answer.
I did not think of $C_c(\mathbb{N})$ as $\mathscr{D}(M)$ for some zero-dimensional manifold $M$ (with countably many connected components), but …