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Month: May 2017

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“What is physical reality?” in my other blog

By Victor Porton
On May 23, 2017

I have published What is physical reality? blog post in my other blog. The post is philosophical.

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#philosophy#physical reality#scientific method
Algebraic general topology Filters General Topology Open problems

A conjecture about funcoids on real numbers disproved

By Victor Porton
On May 22, 2017

I proved that $latex \lvert \mathbb{R} \rvert_{\geq} \neq \lvert \mathbb{R} \rvert \sqcap \geq$ and so disproved one of my conjectures. The proof is currently available in the section “Some inequalities” of this PDF file. The proof isn’t yet thoroughly checked for errors….

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Algebraic general topology Filters General Topology

“Some (example) values” in my book

By Victor Porton
On May 20, 2017

I’ve moved the section “Some (example) values” to my main book file (instead of the draft file addons.pdf where it was previously).

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Formalized math

The math book rewritten with implicit arguments

By Victor Porton
On May 20, 2017

I have rewritten my math book (volume 1) with implicit arguments (that is I sometimes write $latex \bot$ instead of $latex \bot^{\mathfrak{A}}$ to denote the least element of the lattice $latex \mathfrak{A}$). It considerably simplifies the formulas. If you want to be…

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Algebraic general topology Filters General Topology

Values of some concrete funcoids and reloids

By Victor Porton
On May 19, 2017

I’ve calculated values of some concrete funcoids and reloids. The calculations are currently presented in the chapter 3 “Some (example) values” of addons.pdf.

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Algebraic general topology Filters General Topology

New sections in my math book

By Victor Porton
On May 17, 2017

I have added the sections “5.25 Bases on filtrators” (some easy theory generalizing filter bases) and “16.8 Funcoid bases” (mainly a counter-example against my former conjecture) to my math book.

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Algebraic general topology General Topology

The mystery of meet of funcoids solved?

By Victor Porton
On May 14, 2017

It is not difficult to prove (see “Counter-examples about funcoids and reloids” in the book) that $latex 1^{\mathsf{FCD}} \sqcap^{\mathsf{FCD}} (\top\setminus 1^{\mathsf{FCD}}) = \mathrm{id}^{\mathsf{FCD}}_{\Omega}$ (where $latex \Omega$ is the cofinite filter). But the result is counterintuitive: meet of two binary relations is not…

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Algebraic general topology Filters Open problems

Three (seemingly not so difficult) new conjectures

By Victor Porton
On May 9, 2017

I’ve noticed the following three conjectures (I expect not very difficult) for finite binary relations $latex X$ and $latex Y$ between some sets and am going to solve them: $latex X\sqcap^{\mathsf{FCD}} Y = X\sqcap Y$; $latex (\top \setminus X)\sqcap^{\mathsf{FCD}} (\top \setminus Y)…

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  • SCIENCE
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  • Algebraic General Topology
  • Axiomatic Theory of Formulas
  • Limit of a Discontinuous Function
  • More
  • Prize
  • SCIENCE
  • Home
    • Blog
    • Soft
  • Algebraic General Topology
    • Paperback
    • Ebook
    • PDF
  • Axiomatic Theory of Formulas
    • Paperback
    • Ebook
    • PDF
  • Limit of a Discontinuous Function
  • More
    • Donate
    • Review
    • Publish
    • Politics
  • Prize