A breakthrough and getting stuck
I had a very great idea in the field of general topology, what I now call funcoids. Years of my research of funcoids culminated me writing a research monograph about funcoids and related stuff. But after I’ve finished this monograph and submitted it to a publisher, I realize that I get stuck. I have no […]
“Algebraic General Topology. Volume 1” checked for errors
I have finished checking my book “Algebraic General Topology. Volume 1” for errors. That said some minor errors may yet remain, probably I will check it again. At the time of writing this blog post the book is available online. Enjoy this new theory.
Fake alarm: There was no error in my book
I’ve sent my book (Algebraic General Topology. Volume 1) to a publisher. Afterward I’ve withdrawn it due an error. This was a fake alarm: I’ve found an error where there was no error. Today I’ve submitted it to the publisher again. Now (before copyright transfer) the book is available online.
My book “Algebraic General Topology. Volume 1” has a serious error
I found a serious error in my book. The error is in the proof of the lemma currently numbered 15.140. I for now was unable to write a correct proof of this lemma (nor of some appropriate weakening of this lemma). So I’ve withdrawn the book from the publisher.
“Algebraic General Topology. Volume 1” first complete draft
Today I release the first complete (not partial) draft of my book “Algebraic General Topology. Volume 1”. This draft is very rough yet however and needs much editing both for error checking and for greater clarity. It is also possible that I will expand it a little, especially in the chapter “Multifuncoids and staroids”. Download […]
“Algebraic General Topology. Volume 1” – now entire my theory here
The current draft (PDF) of the book “Algebraic General Topology. Volume 1” contains the entire general topology theory which I’ve discovered (so called Algebraic General Topology). Now is a happy day when my entire theory is put into one PDF file (190 A4 pages). In this version of the book are however missing an introductory […]
A readable draft of “Multidimensional Funcoids”
I created a new draft of my article Multidimensional Funcoids article, which is probably has become readable now. Nevertheless there may be many errors yet. Now I am going to concentrate my efforts into putting my research in a book form for participating in EMS Monograph Award.
A change in terminology: multifuncoid -> staroid
I’ve made a change in terminology in my draft article Multidimensional funcoids: multifuncoid → staroid. I now use the term “multifuncoid” in an other sense. I made the change of the terminology in order for the meaning of the term “multifuncoid” to become more similar to the meaning of the term “pointfree funcoid”.
A conjecture about direct product of funcoids
I am attempting to define direct products in the category cont(mepfFcd) (the category of monovalued, entirely defined continuous pointfree funcoids), see this draft article for a definition of this category. A direct product of objects may possibly be defined as the cross-composition product (see this article). A candidate for product of morphisms $latex f_1:\mathfrak{A}\rightarrow\mathfrak{B}$ and […]
“Categories related with funcoids”, a new draft
I started to write a new article Categories related with funcoids. It is now a very preliminary partial draft.