Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Forgot your password?
• Apply for membership

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeSep 2nd 2016
   • PermaLink
   Author: Urs
   Format: MarkdownItexAt _[[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](https://ncatlab.org/nlab/show/Fr%C3%A9chet+space#ProjRInfinity).

   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.

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeSep 4th 2016
   • (edited Sep 4th 2016)
   • PermaLink
   Author: zskoda
   Format: MarkdownItex> (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]].

   (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.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeOct 18th 2017
   • (edited Oct 18th 2017)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added the statement ([here](https://ncatlab.org/nlab/show/Fr%C3%A9chet+space#PathSmoothLinearFunctionsOnFrechetSpaceAreContinuous)) 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.)

   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.)

4. • CommentRowNumber4.
   • CommentAuthornLab edit announcer
   • CommentTimeApr 13th 2019
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexadding dollar signs in spots (such as in the definition of the directional derivative, Frechet spaces F, G) where they are missing cofo <a href="https://ncatlab.org/nlab/revision/diff/Fr%C3%A9chet+space/34">diff</a>, <a href="https://ncatlab.org/nlab/revision/Fr%C3%A9chet+space/34">v34</a>, <a href="https://ncatlab.org/nlab/show/Fr%C3%A9chet+space">current</a>

   adding dollar signs in spots (such as in the definition of the directional derivative, Frechet spaces F, G) where they are missing

   cofo

   diff, v34, current