Questions tagged [locally-convex-spaces]

I'm stuck with the following exercise: Let $(E,\mathcal{P})$ be a metrizable locally convex space. Show that for each sequence $(A_{n})_{n}$ of bounded subsets in $E$ there is a sequence of positive ...

Let $X$ be a locally compact Hausdorff topological space, and let $C_c(X)$ be the space of compactly supported $\mathbf{R}$-valued continuous functions. It is a well-known fact that this space is not ...

Let $X$ be a locally convex space, and $\{Y_i;\ i\in I\}$ a covariant system of locally convex spaces over a partially ordered set $I$, i.e. a system of linear continuous mappings is given $\sigma^j_i:...

We consider a locally compact abelian group $G$. We equip the real vector space $A(G)$ of continuous group homomorphisms $\mathbb{R}\to G$ with the topology of uniform convergence on compact subsets ...

Let $S$ be a set and let $V_s$ be a family of locally convex topological vector spaces (LCSs) indexed by $s \in S$. Let $V$ be a vector space (without topology) and let $T_s:V_s \to V$ be a family of ...