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Algebraic General Topology





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{"ops":[{"insert":"In short: "},{"attributes":{"italic":true},"insert":"I did a math discovery that would be done shortly after 1937 but nobody before me was able to guess during about 60 years. I need money to advance this amazing project further."},{"insert":"\nI do mathematical research in fundamental abstract mathematics on the following topics:\nA new subfield of General Topology, done in an algebraic way. It is a big revolution in mathematics. I think my research is worth prizes of Nobel level. SeeĀ "},{"attributes":{"link":"http://www.mathematics21.org/algebraic-general-topology.html"},"insert":"this page"},{"insert":"Ā for all info about my research. This can be read even by beginning college students, by the way."},{"attributes":{"list":"ordered"},"insert":"\n"},{"attributes":{"link":"http://www.mathematics21.org/formulas.html"},"insert":"Theory of formulas"},{"insert":"Ā (a smaller discovery but also interesting). Mathematicians studied almost everything except of formulas themselves."},{"attributes":{"list":"ordered"},"insert":"\n"},{"insert":"I need money to support my life, buy books, etc., visit scientific conferences.\n"},{"attributes":{"bold":true},"insert":"Project decription"},{"insert":"\n"},{"attributes":{"italic":true},"insert":"Overview"},{"insert":"\nAlgebraic General Topology (= theory of funcoids, reloids, and their generalizations) is a wide generalization of general topology, allowing to express topological properties by algebraic formulas.\nVictor Porton wrote his book \"Algebraic General Topology. Volume 1\" containing a description of this theory (with definitions, theorems, and proofs, as well as expository material allowing its reading by beginning students).\n"},{"attributes":{"italic":true},"insert":"Intellectual Merit"},{"insert":"\nAlgebraic general topology is obviously an exceeding breakthrough because:\nIt is a new big branch of mathematics."},{"attributes":{"list":"bullet"},"insert":"\n"},{"insert":"It is a very general theory based on humorously simple axioms."},{"attributes":{"list":"bullet"},"insert":"\n"},{"insert":"It is expressed in algebraic form, not just a mess of quantifiers as old general topology."},{"attributes":{"list":"bullet"},"insert":"\n"},{"insert":"It contains among other a definition of (generalized) limit of discontinuous function, what is expected to make a revolution in such fields as differential equations."},{"attributes":{"list":"bullet"},"insert":"\n"},{"insert":"The general topology was generalized for an arbitrary kinda multidimensional case (while traditional general topology appeared to be 2-dimensional)."},{"attributes":{"list":"bullet"},"insert":"\n"},{"insert":"The idea of turning a category with additional structure to a semigroup is also novel."},{"attributes":{"list":"bullet"},"insert":"\n"},{"insert":"The definition of funcoid is the biggest discovery in general topology since 1937 (when filters were defined)."},{"attributes":{"list":"bullet"},"insert":"\n"},{"insert":"The work also contains a generalization of filters on posets and other significant discoveries."},{"attributes":{"list":"bullet"},"insert":"\n"},{"insert":"It is a common generalization of calculus and discrete mathematics."},{"attributes":{"list":"bullet"},"insert":"\n"},{"insert":"Common generalization of continuity, uniform continuity, proximal continuity, Cauchy-continuity, discrete continuity."},{"attributes":{"list":"bullet"},"insert":"\n"},{"insert":"It is connecting two previously thought unrelated branches of mathematics: general topology and ordered semigroup/monoid theory. Ordered semigroups are used to describe general topological properties in a novel way; general topology and calculus bring new concepts (such as three kinds of continuity or monovaludness) into ordered semigroup theory."},{"attributes":{"list":"bullet"},"insert":"\n"},{"insert":"Author proposed a new way to define ā€œsidesā€ of manifolds and related things in a more natural way. We previously used the word ā€œsideā€ of a surface but didnā€™t really know what it really is."},{"attributes":{"list":"bullet"},"insert":"\n"},{"insert":"The book is a good studybook. Also it is the world best reference on the topic of filters on posets."},{"attributes":{"list":"bullet"},"insert":"\n"},{"attributes":{"italic":true},"insert":"Broader Impacts"},{"insert":"\nAs author's experience shows that we discover new unexpected results in traditional point-set topology using author's method. This tendency is expected to continue. General topology and thus related branches of science change radically.\n(Generalized) limit of discontinuous function is expected to revolutionize differential equations, integrating, etc. and consequently such natural sciences as physics, engineering, and economics. It also simplifies existing research methods.\nThe project implies broad dissemination of my knowledge to the entire mathematical community to foster further science development.\nThe resulting book can serve as a base of college courses on different topics of algebraic general topology and for a college course on filters on posets and lattices, because it is written as a studybook.\nIf you are a teacher, you can make the following college courses using it as a studybook:\nbasic order theory"},{"attributes":{"list":"bullet"},"insert":"\n"},{"insert":"(co-)brouwerian lattices"},{"attributes":{"list":"bullet"},"insert":"\n"},{"insert":"filters and filtrators"},{"attributes":{"list":"bullet"},"insert":"\n"},{"insert":"funcoids"},{"attributes":{"list":"bullet"},"insert":"\n"},{"insert":"reloids"},{"attributes":{"list":"bullet"},"insert":"\n"},{"insert":"interrelationships between funcoids and reloids"},{"attributes":{"list":"bullet"},"insert":"\n"},{"insert":"multidimensional general topology"},{"attributes":{"list":"bullet"},"insert":"\n"},{"insert":"and more"},{"attributes":{"list":"bullet"},"insert":"\n"},{"insert":"\nP.S. Recently I discovered that many kinds of spaces are ordered semigroup actions: "},{"attributes":{"link":"https://mathematics21.org/the-algebra-of-general-topology/"},"insert":"https://mathematics21.org/the-algebra-of-general-topology/"},{"insert":"\n"}]}

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