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Month: April 2016

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Algebraic general topology Filters General Topology Open problems

An important conjecture about funcoids. Version 2

By Victor Porton
On April 23, 2016

This conjecture appeared to be false. Now I propose an alternative conjecture: Let $latex A$, $latex B$ be sets. Conjecture Funcoids $latex f$ from $latex A$ to $latex B$ bijectively corresponds to the sets $latex R$ of pairs $latex (\mathcal{X}; \mathcal{Y})$ of…

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Algebraic general topology Filters General Topology Open problems

An important conjecture about funcoids

By Victor Porton
On April 23, 2016

Just a few minutes ago I’ve formulated a new important conjecture about funcoids: Let $latex A$, $latex B$ be sets. Conjecture Funcoids $latex f$ from $latex A$ to $latex B$ bijectively corresponds to the sets $latex R$ of pairs $latex (\mathcal{X}; \mathcal{Y})$…

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Algebraic general topology Filters General Topology Open problems

Join of transitive reloids (a conjecture in uniformity theory)

By Victor Porton
On April 21, 2016

Conjecture Join of a set $latex S$ on the lattice of transitive reloids is the join (on the lattice of reloids) of all compositions of finite sequences of elements of $latex S$. It was expired by theorem 2.2 in “Hans Weber. On…

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Algebraic general topology General Topology Open problems

Preservation of properties of funcoids and reloids by their relationships

By Victor Porton
On April 16, 2016

I have added a new section “Properties preserved by relationships” to my math research book. This section considers (in the form of theorems and conjectures) whether properties (reflexivity, symmetry, transitivity) of funcoids and reloids are preserved an reflected by their relationships (functions…

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Algebraic general topology General Topology

New version of my math research book

By Victor Porton
On April 8, 2016

I’ve released a new version of my free math ebook. The main feature of this new release is chapter “Alternative representations of binary relations” where I essentially claim that the following are the same: binary relations pointfree funcoids between powersets Galois connections…

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  • 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