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I discovered Algebraic General Topology (AGT), a new field of math which will replace old General Topology. Mathematical Synthesis is how I call Algebraic General Topology applied to study of Mathematical Analysis.
Please nominate me for Abel Prize.
Below are supplementary articles (Definitions and facts from these articles are used in the articles above.):
See also: Research Plans and Ideas in Algebraic General Topology (an informal document).
Algebraic General Topology is about how to act with abstract topological objects expressing infinities with algebraic operations.
AGT is to math/functional analysis like algebra to old
prose
arithmetic.
Achievements and advantages:
We can now gone with math analysis as now it becomes synthesis, I would say. So I call AGT applied to study of such things as continuousness, limits, and differentials Mathematical Synthesis.
AGT isn't a continuation of former functional analysis research, it is re-research anew beginning almost from scratch. This makes the knowledge level of the First course of a math faculty enough to understand it.
This new research field is both just generalizing former analysis and new theorems/concepts not having analogs in old theories. Several different theorems of analysis often collapse into one AGT equation of which they are obvious consequences.
AGT is very abstract, indeed even the current level of AGT knowledge often allowed me to find simple solutions of practical tasks (such as calculations of infinite sums). I have not yet reached the level of integrals in the synthesis research.
AGT is a kinda thinking with equations. No real numbers analysis expressiveness with visual images preserved. That is not needed anyway as the equations of AGT are even more clear than graphics of old analysis. AGT is simple, natural, and beautiful.
Note that Algebraic General Topology being a generalization of General Topology has nothing in common (except of the name) with Algebraic Topology. Math synthesis is a generalization of functional analysis.
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