Suppose I work over $\mathbb{C}$. Is it known for which locally convex topological vector spaces $V$, we have $\text{Ext}^i(V, \mathbb{C})=\{0\}$ for all $i>0$, working with the type of Ext groups that Wengenroth uses. For instance, is it true when $V$ is Frechet and nuclear?



Ext groups of locally convex topological vector spaces
The Hahn-Banach theorem implies that $\mathbb C$ is an injective object in the category of complex locally convex topological vector spaces. Therefore, Ext$^i(V,\mathbb C)=0$ for every locally convex space $V$.


