Open Problem Garden

Re: Please improve presentation!

I have submitted my 12 open problems to Open Problem Garden (the problems are from the manuscripts of my research). rs has commented on each of the 12 problems the same:

> Please, provide
> 1) definitions of the used concepts (to make the statement self-contained)
> 2) motivation (why this is important, examples, ...)
> At the present state, this text is unfortunately not very useful for someone not acquainted with your manuscripts.

I will not reply 12 times on each comment. Instead I will present my defense here in the suggestion forum. To present definitions of used concepts I would need to repeat a rather lengthly discussion with the definitions under each problem. (And especially I need to explain that I have the reverse order of filters and equating principal filters with sets.) The reader can instead just refer to my online articles. Oh, well this makes my statements not self-contained. But can rs explain why the statements should be self contained? We have hyperlinked Web whose preeminence is in that it allow to make documents not self contained but instead referring to other documents. At the present state, this text is unfortunately not very useful for someone not acquainted with your manuscripts. I agree. But somebody could also claim that an open problem from Graph Theory is bad because the concept of graph is not defined in the problem discussion area. Well, I see the difference, that a typical modern mathematician is supposed to know what is graph but not what is funcoid (from my open problems, only a future mathematician is supposed to know what is funcoid :-) ). But on more abstract level there are no difference, as in both cases the reader must preliminarily acquire himself with some writings. My main idea here is: Better to read the articles anyway. And anyway as in the good case these are read, there are no reason to reprise them in the problem discussion. In the bad case... the reader not understand the problem and surely cannot solve it anyway. Both two cases are considered and in the both cases there are no need for lengthly discussion. So it's proved. Also I agree with rs that I could add some motivation in the problem discussions. I probably will add some motivations to some problems when will have free time. Nevertheless I think that the motivation should be clear for a profound reader of my online articles.