All Questions

Setting: Let $X'$ be a dense subset of an infinite-dimensional Fréchet space $X$ and suppose that $(X_n')_{n \in \mathbb{N}}$ is a nested sequence of non-empty subsets of $X'$ satisfying $$ \bigcup_{n ...

From this post and to (co)completness of the category Top of topological spaces and continuous functions we know that for any diagram $B_i$ and an object $A$ in Top, there are natural maps of sets:$\...

The question is about a fact that is mentioned as "evident" everywhere in the literature, so my guess is that some small detail is passing over my head. Here it is: Let $X_0\hookrightarrow X_1 \...