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At Fréchet space I have added to the Idea-section a paragraph motivating the definition via families of seminorms from the example of $\mathbb{R}^\infty = \underset{\longleftarrow}{\lim}_n \mathbb{R}^n$. And I touched the description of this example in the main text, now here.
(Beware that the same symbol “$\mathbb{R}^\infty$” is also used for the corresponding direct sum/injective limit, which is different.)
Also it is used for the same (“projective”) limit but with $\mathbb{R}^n$ being a dicrete space (what leads to a linearly compact vector space). I added redirect linearly compact vector space to linearly compact module.
I have added the statement (here) that “path smooth” linear functions on a Fréchet space are continuous.
(This sounds like the kind of statement somebody here would already have recorded years back, but I didn’t find it stated in any entry.)
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