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Month: January 2012

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  • 2012
  • January
Filters Publications

My first article is published

By Victor Porton
On January 26, 2012

My first math article (titled “Filters on Posets and Generalizations”) was recently published in a peer reviewed, open access journal. Why I published my first research article only in the age of 31? See my short autobiography.

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#IJPAM#International Journal of Pure and Applied Mathematics
Algebraic general topology General Topology Pointfree topology

Product of two funcoids and product of two funcoids

By Victor Porton
On January 26, 2012

I’ve put online an article (PDF, a partial draft) where I define product of two morphisms for certain categories. (Such products are pointfree funcoids.) Particularly it is defined product of two funcoids and product of two reloids. It is a more mature…

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#categorical product#product
Algebraic general topology General Topology

Some new theorems

By Victor Porton
On January 25, 2012

I added the following theorems to Funcoids and Reloids article. The theorems are simple to prove but are surprising, as do something similar to inverting a binary relation which is generally neither monovalued nor injective. Proposition Let $latex f$, $latex g$, $latex…

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Uncategorized

I am changing my research field

By Victor Porton
On January 12, 2012

I failed to make progress in research of product of funcoids, the next thing I should research in my research plan. I also fail to solve any of my open problems. Thus my research is stalled. I hope other people can solve…

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Algebraic general topology General Topology Open problems

Micronization – the first attempt to define

By Victor Porton
On January 11, 2012

This is my first attempt to define micronization. Definition Let $latex f$ is a binary relation between sets $latex A$ and $latex B$. micronization $latex \mu (f)$ of $latex f$ is the complete funcoid defined by the formula (for every $latex x…

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Algebraic general topology General Topology Open problems

Product funcoids – a first messy draft

By Victor Porton
On January 11, 2012

Product funcoids [outdated link remove] (not a math article but a messy collection of unproved and not exactly formulated statements). This is my first attempt to define product funcoids. There is needed yet much work to rewrite it as a rigorous math…

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Algebraic general topology Filters General Topology

Orderings of filters in terms of reloids, draft

By Victor Porton
On January 2, 2012

I updated the article Orderings of filters in terms of reloids from “preliminary draft” to just “draft”. It means most errors are corrected and now you can read it.

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Algebraic general topology General Topology Open problems

The first problem in the chain is solved

By Victor Porton
On January 1, 2012

I solved the first problem from this blog post (see Funcoids and Reloids article for a solution). It opens the path for solving several other open problems which seem to be its consequences.

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Algebraic general topology General Topology Open problems

Path for solving my open problems

By Victor Porton
On January 1, 2012

I will outline which open problems follow from other open problems. In this post I don’t enter into gory details how to prove these implications, because these are useless without a prior proof of the main premise. I write these notes just…

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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