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Month: July 2015

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Algebraic general topology Filters General Topology Pointfree topology

Another definition of pointfree reloids

By Victor Porton
On July 31, 2015

In previous post I stated that pointfree reloids can be defined as filters on pointfree funcoids. Now I suggest also an alternative definition of pointfree reloids: Pointfree reloids can be defined as filters on products $latex \mathrm{atoms}\,\mathfrak{A} \times \mathrm{atoms}\,\mathfrak{B}$ of atoms of…

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Algebraic general topology Filters General Topology Pointfree topology

Pointfree reloids discovered

By Victor Porton
On July 30, 2015

After I defined pointfree funcoids which generalize funcoids (see my draft book) I sought for pointfree reloids (a suitable generalization of reloids, see my book) long time. Today I have finally discovered pointfree reloids. The idea is as follows: Funcoids between sets…

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Algebraic general topology Filters General Topology Pointfree topology

Binary relations are essentially the same as pointfree funcoids between powersets

By Victor Porton
On July 24, 2015

After this Math.StackExchange question I have proved that binary relations are essentially the same as pointfree funcoids between powersets. Full proof is available in my draft book. The most interesting aspect of this is that is that we can construct filtrator with…

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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