It appears as if all boiled down to find the most appropriate universe of discourse to name the abstract objects I was struggling with.
Here is the story:
This BLOG -to a certain degree- documents work in progress, the construction of a multidimensional book. First-time readers should start at the end, reading first The Challenge and then proceed, unless risking to miss our central point.
The hasty reader may skip the more metaphorical post Génesis or the Biblical Origin of Q-Orders.
The entry Combinatorial Pre-Weyl-Spacesreflects our last consolidated status yet more for initiated readers, i.e. readers who known about the mathematical problems of joining discrete but combinatorial and continuous models. It supersedes older entries, which still may contain interesting heuristics and formula (sometimes with proof).
In Q-Spaces - Examples there are examples, some with pictures that might give an idea of the type of structures e are workin with. Yet is hasn't been updated to the recent status i.e examples remain valid but their presentation will have to change.
The three posts Going in Circles – Part I, Going in Circles – Part II, Going in Circles – Part III, Lines, Cuts and Dedekind should be read in this order unless risking the loss of any deeper understanding.
The BLOG is not -and I'm afraid will never be- like a standard text as published elsewhere or the reference bible for the subject i.e. with lengthy proofs, series of lemmata and finally the big central results.
It's rather a series of essays, the same way I'm used to prepare my classes at university, that is sound in arguments and claims, yet dedicated to induce understanding, not to impress. The carpentería -the carpenters work- to look for proofs etc. etc. I'll leave in my classes as homework, anyway. Some times they come up with counter-examples ...
And I've to admit while I fairly master the task to create curiosity in my students -after 24 years of teaching- I fail completely -may be due to the lack of experience- to write one of those hyper-dense 10 pages journal-articles, that finally only those, who already knew, understand. Recognizing this inability -after 2 years of fruitless intent- was the beginning of this BLOG.