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Month: March 2010

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Algebraic general topology Nonsmooth analysis

Defined limit of discontinuous functions!

By Victor Porton
On March 30, 2010

In my online draft article “Convergence of funcoids” at my Algebraic General Topology site is now defined limit of arbitrary (not necessarily continuous) functions (under certain conditions). Thus mathematical analysis goes to the next stage, non-continuous analysis. Please nominate me for Abel…

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Algebraic general topology Open problems

Erroneous theorem became a conjecture

By Victor Porton
On March 29, 2010

I mistakenly used yet unproved statement that $latex \mathrm{up}\,f$ (taken on the filtrator of funcoids) is a filter for every funcoid $latex f$ in proof of a theorem. So after I found this error I downgrade this theorem to the status of…

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#error
Algebraic general topology

Erroneous lemma corrected

By Victor Porton
On March 29, 2010

In “Funcoids and Reloids” online draft there was an erroneous lemma: Lemma For every two sets $latex S$ and $latex T$ of binary relations and every set $latex A$ $latex \bigcap {\nobreak}^{\mathfrak{F}} S = \bigcap {\nobreak}^{\mathfrak{F}} T \Rightarrow \bigcap {\nobreak}^{\mathfrak{F}} \{ \langle…

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#error
Algebraic general topology

Errors in Funcoids and Reloids corrected

By Victor Porton
On March 28, 2010

I corrected some errors in “Funcoids and Reloids” online draft. The main error was messing $latex \subseteq$ and $latex \supseteq$ in the theorem about continuing a function defined on atomic filter objects till $latex \langle f\rangle$ for a funcoid $latex f$ (currently…

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#error
Filters Publications

Resubmit to Documenta Mathematica

By Victor Porton
On March 27, 2010

I submitted the preprint of my article “Filters on Posets and Generalizations” to Documenta Mathematica math journal but so far received no reply. So I sent submission to an other editor of the same journal.

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#Documenta Mathematica
Algebraic general topology Open problems

False proof of an open problem

By Victor Porton
On March 27, 2010

I earlier proclaimed that I positively solved this conjecture: Conjecture $latex f\cap^{\mathsf{FCD}} g = f\cap g$ for every binary relations $latex f$ and $latex g$. There were error in my proof and I deleted it. See the draft of Funcoids and Reloids…

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#error
Algebraic general topology Open problems

New conjectures about complete funcoids and reloids

By Victor Porton
On March 26, 2010

After removing an erroneous theorem I posed two new open problems to take its place: Conjecture If $latex f$ is a complete funcoid and $latex R$ is a set of funcoids then $latex f \circ \bigcup {\nobreak}^{\mathsf{FCD}} R = \bigcup {\nobreak}^{\mathsf{FCD}} \langle…

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Algebraic general topology

Erroneous theorem

By Victor Porton
On March 26, 2010

I found a counter-example and an error in my proof of this (erroneous) theorem in Funcoids and Reloids article: Let $latex f\in\mathsf{FCD}$. If $latex R$ is a set of co-complete funcoids then $latex f \circ \bigcup {\nobreak}^{\mathsf{FCD}} R = \bigcup {\nobreak}^{\mathsf{FCD}} \left\langle…

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#error
Algebraic general topology Open problems

“Funcoids and Reloids” contains “Connectedness”

By Victor Porton
On March 25, 2010

Now Funcoids and Reloids online article contains the section “Connectedness regarding funcoids and reloids” which previously was in a separate article. In this section there are among definitions and theorems a few open problems.

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#connected space#connectedness#connectivity
Algebraic general topology Filters Open problems

Errors corrected in article “Connectedness of funcoids and reloids”

By Victor Porton
On March 25, 2010

I have said that there were several errors in my draft article “Connectedness of funcoids and reloids” at Algebraic General Topology site. I have corrected the errors, but now some of what were erroneous theorems downgraded to the status of conjecture.

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#connected space#connectedness#connectivity

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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