Skip to content

    Math Research of Victor Porton

    Because I didn't succeed to publish my 457 pages article stuck in half-published state (I didn't succeed by parts, too), I plead with God to destroy mankind, that lost ordered semigroup actions, and create a new civilization from me. I can't get a publication grant, because I have no scientific degree. I didn't finish a university course because of religious discrimination. You don't pay for me taking a university course again because of your greed. Conclusion: Mankind dies because of infinite greed of just one human, you.

    • SCIENCE
      • Journal with post-moderation
      • World Science DAO
    • Home
      • Blog
      • Soft
    • Algebraic General Topology
      • Paperback
      • Ebook
      • PDF
    • Axiomatic Theory of Formulas
      • Paperback
      • Ebook
      • PDF
    • Discontinuous Analysis
      • Full Course
    • More
      • Donate
      • Review
      • Publish
      • Politics
    • Prize

    Month: March 2011

    • Home
    • 2011
    • March
    Algebraic general topology Filters General Topology

    Two elementary theorems

    By Victor Porton
    On March 30, 2011

    I proved the following two elementary but useful theorems: Theorem For every funcoids $latex f$, $latex g$: If $latex \mathrm{im}\, f \supseteq \mathrm{im}\, g$ then $latex \mathrm{im}\, (g\circ f) = \mathrm{im}\, g$. If $latex \mathrm{im}\, f \subseteq \mathrm{im}\, g$ then $latex \mathrm{dom}\,…

    read more
    Algebraic general topology General Topology

    Funcoid corresponding to a monovalued reloid is monovalued

    By Victor Porton
    On March 29, 2011

    I proved the following simple theorem: 1. $latex (\mathsf{FCD}) f$ is a monovalued funcoid if $latex f$ is a monovalued reloid. 2. $latex (\mathsf{FCD}) f$ is an injective funcoid if $latex f$ is an injective reloid. See online article “Funcoids and Reloids”…

    read more
    Algebraic general topology Filters General Topology

    New corollary

    By Victor Porton
    On March 29, 2011

    To the theorem “Every monovalued reloid is a restricted function.” I added a new corollary “Every monovalued injective reloid is a restricted injection.” See the online article “Funcoids and Reloids” and this Web page.

    read more
    Algebraic general topology General Topology Pointfree topology

    “Pointfree Funcoids” is now a good draft

    By Victor Porton
    On March 26, 2011

    I updated online article “Pointfree Funcoids” from “preliminary draft” to just “draft”. This means that it was somehow checked for errors and ready for you to read. (No 100% warranty against errors however.) Having finished with that draft the way is now…

    read more
    Algebraic general topology General Topology Pointfree topology

    Draft: Pointfree funcoids

    By Victor Porton
    On March 23, 2011

    My draft article Pointfree Funcoids was not yet thoroughly checked for errors. However at this stage of the draft I expect that there are no big errors there only possible little errors. Familiarize yourself with Algebraic General Topology.

    read more
    Algebraic general topology General Topology

    Completion of a join of reloids

    By Victor Porton
    On March 18, 2011

    I proved true the following conjecture: Theorem $latex \mathrm{Compl} \left( \bigcup^{\mathsf{RLD}} R \right) = \bigcup ^{\mathsf{RLD}} \langle \mathrm{Compl} \rangle R$ for every set $latex R$ of reloids. The following conjecture remains open: Conjecture $latex \mathrm{Compl}\,f \cap^{\mathsf{RLD}} \mathrm{Compl}\,g =\mathrm{Compl} (f \cap^{\mathsf{RLD}} g)$ for…

    read more
    Algebraic general topology Filters General Topology

    Compl CoCompl f = CoCompl Compl f = Cor f

    By Victor Porton
    On March 18, 2011

    I proved true the following conjecture: Theorem $latex \mathrm{Compl} \, \mathrm{CoCompl}\, f = \mathrm{CoCompl}\, \mathrm{Compl}\, f = \mathrm{Cor}\, f$ for every reloid $latex f$. See here for definitions and proofs.

    read more
    #completion#reloids
    Algebraic general topology General Topology

    Yet two simple theorems

    By Victor Porton
    On March 17, 2011

    I proved the following two simple theorems: Proposition $latex \mathrm{Compl}f = \bigcup^{\mathsf{FCD}} \left\{ f|^{\mathsf{FCD}}_{\{ \alpha \}} \middle| \alpha \in \mho \right\}$ for every funcoid $latex f$. Proposition $latex \mathrm{Compl}f = \bigcup^{\mathsf{RLD}} \left\{ f|^{\mathsf{RLD}}_{\{ \alpha \}} \middle| \alpha \in \mho \right\}$ for every…

    read more
    Algebraic general topology General Topology

    Two similar theorems about funcoids and reloids

    By Victor Porton
    On March 17, 2011

    I proved the following two similar theorems about funcoids and reloids: Theorem For a complete funcoid $latex f$ there exist exactly one function $latex F \in \mathfrak{F}^{\mho}$ such that $latex f = \bigcup^{\mathsf{FCD}} \left\{ \{ \alpha \} \times^{\mathsf{FCD}} F(\alpha) | \alpha \in…

    read more
    Uncategorized

    Restricting a reloid to a trivial atomic filter object

    By Victor Porton
    On March 17, 2011

    I proved the following (not very hard) theorem: Theorem $latex f|^{\mathsf{RLD}}_{\{ \alpha \}} = \{ \alpha \} \times^{\mathsf{RLD}} \mathrm{im} \left( f|^{\mathsf{RLD}}_{\{ \alpha \}} \right)$ for every reloid $latex f$ and $latex \alpha \in \mho$. See the online article about funcoids and reloids.

    read more

    Posts navigation

    1 2 Next
    Top

    Copyright © 2023 Math Research of Victor Porton - WordPress Theme : By Sparkle Themes

    • SCIENCE
    • Home
    • Algebraic General Topology
    • Axiomatic Theory of Formulas
    • Discontinuous Analysis
    • More
    • Prize
    • SCIENCE
      • Journal with post-moderation
      • World Science DAO
    • Home
      • Blog
      • Soft
    • Algebraic General Topology
      • Paperback
      • Ebook
      • PDF
    • Axiomatic Theory of Formulas
      • Paperback
      • Ebook
      • PDF
    • Discontinuous Analysis
      • Full Course
    • More
      • Donate
      • Review
      • Publish
      • Politics
    • Prize