Algebraic General Topology. Vol 1: Paperback / E-book || Axiomatic Theory of Formulas: Paperback / E-book

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Abstract. How a sectarian fanatic discovered a breakthrough formula. Also
a story of appearance of a new religion. And a lawsuit on mathematics.
1. Where the research is published
I have recently published most of my main discoveries in research monograph [2].
I started to write a second edition with more advanced axiomatics.
Before that I’ve published just one article [1]. As you see below I am an amateur
mathematician, not a professor.
2. What I discovered
I discovered a generalization of general topology that allows to express topolog-
ical properties with algebraic formulas. Later I also discovered (generalized) limit
of discontinuous function and kinda multidimensional general topology (as well as
some other things).
The “start point” of algebraic general topology was the formula
(1) αX u Y 6= βY u X 6= ,
where α is a function from the set of filters on a set A to the set of filters on a
set B, β is a function from the set of filters on a set B to the set of filters on a
set A, X and Y are filters on these sets. u is the meet operation on the lattice of
filters ordered reverse to the set theoretic inclusion and is the improper filter.
Now I call a pair (α, β) conforming to the above as funcoid.
It is algebraic general topology, because it is easy to find an operation that
makes the set/class of funcoids into a semigroup or precategory (exercise! or read
my book).
At this point my serious mathematical journey started.
3. Story of the discovery
I was a Protestant.
I deemed that I should openly proclaim my faith: (Luk. 9:26) “For whoever shall
be ashamed of me and of my words, of him shall the Son of man be ashamed, when
he shall come in his own glory, and in his Father’s, and of the holy angels.” and
Mrk. 8:38.
Moreover, I “reduced” my confession: “I am a sectarian”, “I am a religious
fanatic.” I considered the word “sectarian” as one of the Christ’s words, because
the Gospel, 2Cor. 6:17 contains the word “separate”, the root of which has the
same meaning as the roots of the words “sectarian” and “holy”. I considered the
word “fanatic” to be one of Christ’s words, because the Bible says (Rev. 3:19) “be
zealous” and “jealous” and “fanatic” are words with the root of a similar meaning.
My so-called “confession of faith” caused a sharply negative reaction of people
and led to religious discrimination, refusal to talk to me, insults, and often beatings.
Moreover, realizing the hopelessness of my situation, I did not even try to improve
my social status, since this was clearly impossible. In addition, with such my
position, new opportunities would mean new problems for me.
When I was a first year student at Perm State University, I became interested
in general topology and set a goal to discover algebraic general topology.
So I ended up on the street, without food. I began to eat grass and drink from
a puddle and wait for death from hunger (as you know, I still survived).
From nothing to do, I continued my mathematical thoughts and came up with
the formula (1). The biggest math discovery in general topology since 1937 (when
the filters were discovered) was made by a hungry homeless on the street.
I wrote a term paper with this formula and some theorems about it at my first
year opening in the university.
Understanding that a religious fanatic cannot find a job and for me it is threat-
ening soon again starvation and death, I decided to show humility: become eco-
nomically weaker (abandon my economic goals and ambitions) in order to become
richer. To become economically weaker, I decided to leave the university in the 5th
year and filed a deduction.
My humility worked: I managed to get a second disability group that provided
the conditions for my survival. Besides other things, I told psychiatrists that I have
a strange object in my brain, a seraph (“genius” in Greek mythology). Consider
both options: if I have a foreign object in my brain then I’m a disabled person in
the psyche, if not then disabled in the psyche, too.
4. Lawsuit
As you know, I wrote a doctoral dissertation in mathematics [2] and I was not
awarded the title of Doctor of Science for religious reasons as a punishment for
practicing my religion.
I sued, demanding compensation for the unpaid salary of a professor of mathe-
matics and other things, as well as 4 trillion dollars as compensation for not made
due to poverty scientific discoveries. (I valued this book along with amendments,
as well as my XML file processing method in 2 trillion dollars; well, how much is
the limit of the discontinuous function?)
It was not that court, and after that I filed a lawsuit in the Tverskoy court of
Moscow. This time without the requirement of 4 trillions and the title of hero of
But when she saw the word “sectarian”, the chairman of the court, Olga Niko-
laevna Solopova, went crazy with laughter and shame and, deciding that humor
took precedence over the law, did not respond to my lawsuit. It is clear that
Solopova cannot answer, therefore I demanded that the qualification collegium of
judges recognize her as incompetent and insane as a result of exposure to her brain
with information about an abnormal sectarian and transfer the case to another
judge. Qualification board responded that there is no record in their database.
(Apparently insane of laughter Solopova threw the document into the trash.) Such
should be the reaction of a judge to a suit of a subhuman, in accordance with
Note: I’m not going to actually bankrupt Russia.
5. My religious development
So dying of hunger (I ate grass that time) on the streets I discovered a trillion
dollars worth (in my own estimation) formula.
I thought “If I don’t lie and deny my religion, I will bring a trillion dollars formula
to the coffin.”
Isn’t to bury a talent a sin? If I kill myself with repeatedly saying that I am a
sectarian, it would harm a great number of people, thought I.
I thought also: If I’d become a prostitute to survive, I’d just have sex with
somebody who does not want to have sex with, but if I save my formulas, I would
probably help to develop Internet and dating sites, thus allowing many people to
have sex with whom they want. So I am an egoist.
Nonsense? Exactly, I knew something was wrong in my religion.
After many failures I conceived a new religion.
Here my new religion in the most general form I know now: The will of Christ
is imperfect (as He prays “not my will but Yours to be done”) and we should serve
directly the Father, stop following the will of Christ and follow the will of the Father
directly. The New Testament (“new contract”, literally) is self-terminated.
I wrote a book on this topic:
To serve Christ means to serve truth (He said “I am truth.” meaning essentially,
“I am mathematics.”) that is to try to never say a lie. This is wrong: If I am a
Jew and I’d meet fascists, I’d to say them I am not a Jew. Or I could lie that I am
not a sectarian to survive (and am I really not a sectarian now?)
6. Conclusion
This is the story of a trillion dollars (accordingly my own estimation) formula
by a first year student and a new religion.
About mathematical aspects of the story of my discoveries, see blog post:
[1] Victor Porton. Filters on posets and generalizations. International Journal of Pure and Applied
Mathematics, 74(1):55–119, 2012.
[2] Victor Porton. Algebraic General Topology. Volume 1. INFRA-M, 2019.