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Month: February 2018

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Algebraic general topology Filters General Topology Open problems

Join of two connected (regarding a funcoid) filters, whose meet is proper, is connected

By Victor Porton
On February 14, 2018

I have proved that join of two connected (regarding a funcoid) filters, whose meet is proper, is connected. (I remind that in my texts filters are ordered reverse set-theoretic inclusion.) The not so complex proof is available in the file addons.pdf. (I am…

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Algebraic general topology Filters General Topology Open problems

More on connectedness of filters

By Victor Porton
On February 14, 2018

I added more on connectedness of filters to the file addons.pdf (to be integrated into the book later). It is a rough incomplete draft. Particularly the proof, that the join of two connected filters with proper meet is connected, is not complete. (Remember…

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Algebraic general topology Filters General Topology

Connectedness of funcoids and reloids – an error corrected

By Victor Porton
On February 13, 2018

I have corrected some errors in my book about connectedness of funcoids and reloids. In some theorems I replace like $latex S(\mu)$ with $latex S_1(\mu)$ and arbitrary paths with nonzero-length paths. I also discovered (not yet available online) some new results about connected…

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Uncategorized

Please nominate me for Breakthrough Prize in mathematics

By Victor Porton
On February 7, 2018

Please read my math research and decide if it is worth the prize. If you consider my research worth the prize, please nominate me. Nominations for the Breakthrough Prize and New Horizons Prize in mathematics are now open. The Breakthrough Prize in…

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Algebraic general topology Filters Open problems

Counting sides of a surface topologically

By Victor Porton
On February 5, 2018

I have defined sides of a surface (represented by such things as a set in a topological space) purely topologically. I also gave two (possible non-equivalent) definitions of special points of a surface (such “singularities” as points of the border of a…

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Algebraic general topology General Topology

ERROR: Section “Micronization” removed

By Victor Porton
On February 2, 2018

“Micronization” was a thoroughly wrong idea with several errors in the proofs. This section is removed from the book.

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Algebraic general topology General Topology

Error in my math book

By Victor Porton
On February 1, 2018

I’ve noticed that the statement “Micronization is always reflexive.” in my math book is erroneous. It led also to some further errors in the section “Micronization”. I am going to correct the errors in near time.

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  • SCIENCE
  • Home
  • 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