have made certain math discoveries. I deem these worth $1000000 prize (Abel Prize for mathematicians). I didn’t receive a scientific degree for discrimination reasons, please help me to have the money.

**Please help me to receive this prize.** I ask you to nominate me for this prize (to fill a certain Web form). *Please also nominate me for Mathematics Breakthrough Prize (you need an independent recommendation of my work for the second prize, no need of such for the Abel Prize).*

## How to Nominate Me

If you want to help me, please fill this form.

Note that in order for participating in the nomination of this year, the letter should be send before September 1th. (If you send it later the nomination will be delayed to the next year.)

## The Content of the Letter

The letter shall contain at least the following information:

- my CV (copy it from below);
- the description of my math discoveries and the list of my articles (see below);
- a list of leading specialists in General Topology (see below for such a list).

### The Nominee’s CV

(Include this into your letter to the Academy.)

- Full name
- Victor Lvovich Porton
- Year of birth
- 1980
- Place of birth
- city Perm, Russia
- Education
- Unfinished* Mechanics and Mathematics faculty of Perm State University (state Perm, Russia).
- Scientific degrees
- None
- Teaching and research experience
- No teaching experience. Research experience consists of doing research published on www.math.portonvictor.org Web site and development of a new way to process XML data.
- Publications

- Victor Porton. Filters on posets and generalizations. International Journal of Pure and Applied Mathematics, 74, No. 1 2012.
- Victor Porton. Algebraic General Topology. 2019. INFRA-M.

Email: porton@narod.ru

Address: Shay Agnon 32-29, Ashkelon, Israel, 7864022

Phone: +972-545229306

* I have not finished the University because has gone to an (engineering) job instead of receiving a degree for the reasons of religious discrimination.

### The Description of Nominee’s Math Research

The research of Victor Porton is presented in research monographs:

- Victor Porton.
Algebraic General Topology. Volume 1

- Algebraic General Topology. Book 3: Algebra
- Limit of a Discontinuous Function

See also online articles (superseded by the above monograph):

- Funcoids and Reloids – http://www.math.portonvictor.org/binaries/funcoids-reloids.pdf.
- Convergence of Funcoids – http://www.math.portonvictor.org/binaries/limit.pdf.
- Pointfree Funcoids – http://www.math.portonvictor.org/binaries/nary.pdf.
- Orderings of filters in terms of reloids – http://www.math.portonvictor.org/binaries/filters-order.pdf.
- Multidimensional Funcoids – http://www.math.portonvictor.org/binaries/nary.pdf.

At the author’s site there are also published the following supplementary materials (in a very rought draft state):

- Algebraic General Topology. Volume 1 addons (about relations of the author’s research with more advanced classical mathematics (particularly of category theory) than used in the volume 1)
- Algebraic General Topology. Volume 2 partial draft

The addons and unpublished Git sources contain among other things started rewriting of the theory with more general semigroups instead of naive use of category theory. It is based on author’s theory of transforming categories with certain additional structure into semigroups.

I suggest to attach the above mentioned PDF files (especially the book) to your nomination email.

#### Principal contributions for which the candidate(s) is/are nominated:

They are introduced new concepts of funcoids and reloids generalizing correspondingly proximity spaces and uniform spaces and profoundly researched their properties, so creating the most general theory in point-set topology. (It’s opened up a new major research area.) The new theory is much more algebraic than traditional general topology.

Both continuity and uniform continuity as well as proximity continuity are re-formulated as algebraic formulas generalizing all three kinds of continuity and hiding the epsilon-delta notion behind algebraic formulas.

It’s defined the notion of limit for arbitrary (not necessarily continuous) functions. Moreover it is defined for arbitrary multivalued functions and even for an arbitrary funcoid. It makes trivial to define the derivative of an arbitrary function, integral of an arbitrary function, etc. Based on this, there is defined the space of nondifferentiable solutions of a differential equation.

Also pointfree funcoids and multidimensional funcoids (generalizations of funcoids) and several products (both finitary and infinitary) (cross-composition product, product of anchored relations, displaced product, ordinated product, simple product) of funcoids and other morphisms are introduced and the foundation of their theory is laid.

Accordingly Google, the author is the first person who considered ordered semigroup actions and ordered precategory actions. The author has shown that elements of ordered semigroup actions are “spaces”, a generalization simultaneously of topological, (quasi)uniform, (quasi)proximity, and (quasi)metric spaces, (directed) graphs, etc. Ordered precategory actions can be compared in importance to group theory.

#### Brief description of candidate’s work:

It is written the book “Algebraic General Topology. Volume 1”.

The book contains the following materials:

- common knowledge (order and lattice theory, including Galois connections and co-brouwerian lattices; short introductions into category theory and group theory);
- candidate’s own study of some more things about order theory;
- theory of filters on posets and their generalization “filtrators”;
- short description of customary (traditional) general topology: metric spaces, topological spaces, pretopological spaces, preclosures, proximity spaces;
- theory of funcoids (the definition of funcoids is a candidate’s discovery), including: composition of funcoids, co-brouwerian lattices of funcoids, some categories related with funcoids, atomic funcoids, complete funcoids and completion of funcoids, monovalued and injective funcoids, and other;
- theory of reloids (filters on cartesian products of sets), including: composition of reloids, some categories related with reloids, complete reloids and completion of reloids, monovalued and injective reloids, and other;
- relationships between funcoids and reloids (it is shown that these are related with certain Galois inclusions and some other mappings);
- general theory of continuous morphisms (for a partially ordered category);
- connectedness of sets or filters regarding funcoids and reloids;
- total boundness of reloids (generalizing total boundness of uniform spaces);
- application of the theory of reloids for comparing (with certain partial orders) of filters on sets;
- pointfree funcoids (a trivial generalization of funcoids);
- convergence and limit for funcoids, generalized limit for arbitrary funcoids;
- star categories (certain categories with an additional structure);
- generalizations of pointfree funcoids and reloids:
- staroids;
- multifuncoids;
- infinite products of elements;
- multireloids;

- (finitary and infinitary) products of funcoids:
- cross-composition product;
- simple product;
- displaced product;
- subatomic product;
- other.

- so called “spaces” that is elements of ordered semigroup actions that are generalization simultaneously of topological, (quasi)uniform, (quasi)proximity, and (quasi)metric spaces, (directed) graphs, etc.
- most of general topology concepts (continuity, limit, openness, closedness, hausdorffness, compactness, connectedness, etc.) directly generalize in terms of spaces;
- spaces are generalized to elements of ordered precategory actions.

The candidate has proposed several new open problems.

### List of math specialists

The following is a list of a few General Topology specialists. (Note that I am not personally or in any other way connected with the listed specialists. I have found their names using Internet.)

- Bob Lowen and his wife, Eva Colebundes (specialists in proximity spaces);
- V.V.Fedorchuk, M.V.Smurov, Yu.V.Sadovnichii (specialists in uniform topology);
- M. Hušek and J. van Mill (authors of
Recent Progress in General Topology II

book); - K.P. Hart, Jun-iti Nagata, J.E. Vaughan (authors of
Encyclopedia of General Topology

book); - Hans-Peter A. K¨unzi (a specialist in quasi-uniform spaces);
- I. M. James (author of
Introduction to Uniform Spaces

andTopological and Uniform Spaces

books); - Ryszard Engelking (author of some works in general topology);
- John L. Kelley (author of
General Topology

book); - Stephen Willard (author of
General Topology

book); - Mangesh Ganesh Murdeshwar (author of
General topology

book); - Horst Herrlich (specialist in categorical topology);
- Paul Taylor (inventor of Abstract Stone Duality);

## Frequently Asked Questions

*What is Abel Prize?*

It is an about $1000000 prize, like Nobel Prize, but for

mathematicians (Nobel Prize is for other sciences).

*Why don’t you nominate yourself, but ask others to do this?*

Abel Prize rules forbid self-nominations.

*Why do you want Abel Prize?*

- Having a million dollars, I won’t have anymore the necessity to earn my living as a programmer and will be able to dedicate all my time to more important things including mathematics, information technology, and free software development.
- Receiving Abel Prize will make my research famous among mathematicians, as it should be.

*Is it OK that I nominate you after your plea to nominate rather than by my own initiative?*

Yes, it is OK, as long as *you do not contact me about nominating.*

*When to nominate?*

If possible, please nominate before September 1th (if doubt fill the form now).

*Should I notify you after I nominate you?*

**No!** Don’t tell me that you have nominated me! It would contradict Abel Prize rules. Do not ask me any questions about Abel Prize, do not mention in any way that you are going to nominate me.

*What if somebody other except me nominates you?*

To be sure that I will be nominated please nominate me. It will not harm if I will be nominated several times.

*What will I receive in return?*

Sorry, nothing. (I can’t pay you a part of money because the nominations are confidential and I don’t have to know that you nominated me.) Please make a goodwill to help me.

*Is it significant that you have no official scientific degree?*

No, this should be not important. Really I have almost finished math education in an University. (I left the University because has gone to a job and because of a discrimination.) The official Abel Prize rules do *not* require the nominee to have a scientific degree.

(Actually if they would use scientific degree as a criterion for selecting the laureate, it would be a serious violation of the committee rules which require other criteria such as influence of the work on the development of science, not degrees and social position what would be a clear discrimination.)

*How will you use the money?*

First, I promised to donate $10000 to PlanetMath site and $10000 to TeXmacs program after I will win Abel Prize.

I will put the rest of money to deposits or shares or something similar. I am also going to invest into books which I’ll write.

I plan to resettle to a hotel for my basic needs to be fulfilled, or maybe to buy an apartment in a good place.

I am going to use the most of the rest of the benefit for charity (either support of poor people or support of scientific/technological development or both).