Algebraic general topology – what is it?
First, what is a general topology? General topology is the theory of topological spaces, as well as uniform spaces, proximity spaces, and metric spaces.
I made a rather big discovery – a general theory that generalizes all these types of spaces in one algebra. That is, instead of four theorems about each of these spaces, we get one.
I called my theory “algebraic general topology”. Algebraic, because instead of the nightmare confusion of logical reasoning from the traditional general topology, we have simple algebraic formulas. Visit my site where you can find these formulas.
I discovered the first formula of algebraic general topology when I was in my first year at the Faculty of Mathematics. For several months I thought, removing unnecessary axioms, and suddenly I understood this first formula. Now I call this formula the definition of a funcoid. That is, funcoids are determined by just one axiom. Again, go to my site.
Then I added what I call reloids – just filters on the Cartesian product of two sets.
It turns out a very interesting theory: funcoids, reloids, connections between them, their generalizations, etc. Much more interesting than the traditional general topology.
Funcoids and reloids can be combined. The resulting operation “composition” (named by analogy with the composition of functions) is associative. Such a structure is called a semigroup. This is an algebraic structure and the properties of funcoids, such as, for example, continuity are described by algebraic formulas. Moreover, this also works, for example, for multi-valued functions.
Not so long ago, I realized that, moreover, any spaces are actions of ordered semigroups. Even funcoids and reloids are just a special case of my new theory. What is funny, before me there was not a single article on the Internet about actions of ordered semigroups.
Combining elements such semigroups can write the formula of what I call the generalized limit. This “enhanced” limit can be applied to any function, even discontinuous. Don’t interrupt viewing of this video: the limit of the discontinuous function does not exist – that means the author is a pseudo-scientist. I am talking about a generalized limit, not the usual one.
So in my system, any function has a limit, which means that any function has a derivative and an integral. Did you hear what I said? You must be in shock. Moreover, I also gave a definition of non-differentiable solutions of differential equations. This is called the phrase “science of the future”.
All information on algebraic general topology and the limit of a discontinuous function, with all the proofs, is available in the books on my site.
And everything is explained so that even a novice student could understand.
So, read my books and find out, finally, about the analysis on filters. Type in Google algebraic general topology. Do not forget to like this video: support the science of the future. Send money and Bitcoins. But most importantly, read my books.
Learn more about Algebraic General Topology here.