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1. • CommentRowNumber1.
   • CommentAuthorporton
   • CommentTimeSep 12th 2013
   • (edited Sep 12th 2013)
   • PermaLink
   Author: porton
   Format: MarkdownItexI have created page <a href="http://nlab.mathforge.org/nlab/show/funcoid">funcoid</a> on nLab wiki. After this I was meet with <a href="http://nforum.mathforge.org/discussion/3911/">some harsh</a>. <blockquote><p>Otherwise, we see you as a stranger writing in our lab book, so to speak, and your stuff will probably just be erased in the end.</p></blockquote> One quote from that conversation: <blockquote><p>Avoiding mention of ϵs and δs is old hat, but cartesian closed categories of spaces are not.</p></blockquote> A few days ago I have proved that my category $\mathbf{Fcd}$ ((proximally) continuous maps between endofuncoids) has all small products and all small co-products. See <a href="http://www.mathematics21.org/binaries/product.pdf">this draft article</a>. Today I've tried to prove that it is cartesian closed (has exponentials) but without much success. By the way, the category $\mathbf{Top}$ can be embedded (in a non-technical sense) into my $\mathbf{Fcd}$ at least in two ways (as Kuratowski closures and as systems of neighborhood filters). This makes my category probably useful for customary general topology (among of properties of $\mathbf{Fcd}$ being interesting by themselves). I ask the nLab authorities to hold back your harsh and allow me to post my stuff into your wiki site. One purpose for this is to distribute my open problem whether $\mathbf{Fcd}$ is cartesian closed ("new hat"). I am not sure whether I am able to solve this myself. Trying together would surely be better. For others to see my research result would also be an advantage. In the meantime, I will probably resign from attempt to investigate whether it is cartesian closed and instead concentrate on researching properties of funcoids similar to compactness of topological spaces. BTW, it is quite likely that $\mathbf{Fcd}$ is even smoother (has more smooth "algebraic properties") than an ordinary cartesian closed category. But the time to investigate this has not yet come. Let lay it as a way for future research in nLab wiki.

   I have created page funcoid on nLab wiki.

   After this I was meet with some harsh.

   Otherwise, we see you as a stranger writing in our lab book, so to speak, and your stuff will probably just be erased in the end.

   One quote from that conversation:

   Avoiding mention of ϵs and δs is old hat, but cartesian closed categories of spaces are not.

   A few days ago I have proved that my category $\mathbf{Fcd}$ ((proximally) continuous maps between endofuncoids) has all small products and all small co-products. See this draft article.

   Today I’ve tried to prove that it is cartesian closed (has exponentials) but without much success.

   By the way, the category $\mathbf{Top}$ can be embedded (in a non-technical sense) into my $\mathbf{Fcd}$ at least in two ways (as Kuratowski closures and as systems of neighborhood filters). This makes my category probably useful for customary general topology (among of properties of $\mathbf{Fcd}$ being interesting by themselves).

   I ask the nLab authorities to hold back your harsh and allow me to post my stuff into your wiki site. One purpose for this is to distribute my open problem whether $\mathbf{Fcd}$ is cartesian closed (“new hat”). I am not sure whether I am able to solve this myself. Trying together would surely be better. For others to see my research result would also be an advantage.

   In the meantime, I will probably resign from attempt to investigate whether it is cartesian closed and instead concentrate on researching properties of funcoids similar to compactness of topological spaces.

   BTW, it is quite likely that $\mathbf{Fcd}$ is even smoother (has more smooth “algebraic properties”) than an ordinary cartesian closed category. But the time to investigate this has not yet come. Let lay it as a way for future research in nLab wiki.

2. • CommentRowNumber2.
   • CommentAuthorMike Shulman
   • CommentTimeSep 12th 2013
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexAs far as I can see, all the objections raised at that discussion still apply.

   As far as I can see, all the objections raised at that discussion still apply.

3. • CommentRowNumber3.
   • CommentAuthorTobyBartels
   • CommentTimeSep 13th 2013
   • PermaLink
   Author: TobyBartels
   Format: MarkdownItexI would particularly suggest following the steps in (2) and (13) (probably in reverse order) from the ‘harsh’ thread.

   I would particularly suggest following the steps in (2) and (13) (probably in reverse order) from the ‘harsh’ thread.

4. • CommentRowNumber4.
   • CommentAuthorTodd_Trimble
   • CommentTimeSep 13th 2013
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexI think #2 from the "harsh" thread is most directly relevant to wanting to write on the nLab. There are occasions where we offer someone a personal web on the nLab complex to record personal research, but that person would have to have established himself or herself first, either via public consensus on strength of publications, or on strength of contributions to the nLab.

   I think #2 from the “harsh” thread is most directly relevant to wanting to write on the nLab. There are occasions where we offer someone a personal web on the nLab complex to record personal research, but that person would have to have established himself or herself first, either via public consensus on strength of publications, or on strength of contributions to the nLab.