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Month: April 2010

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Algebraic general topology Pointfree topology

My research plans shifted

By Victor Porton
On April 23, 2010

Yesterday I wrote that I next thing which I will research are n-ary funcoids and n-ary reloids. It seems that (n+m)-ary funcoid can be split into a funcoid acting from n-ary funcoids to m-ary funcoids (similarly to (n+m)-ary relation can be split…

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Algebraic general topology Nonsmooth analysis

My research plan

By Victor Porton
On April 23, 2010

I ‘ve said that I take a vacation in my math research work in order to write a religious book. Unexpectedly quickly I have already finished to write and publish this book and return to my mathematical research. Now having researched enough…

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Algebraic general topology

Funcoids and reloids, a Galois connection

By Victor Porton
On April 23, 2010

I proved that $latex (\mathsf{FCD})$ is the lower adjoint of $latex (\mathsf{RLD})_{\mathrm{in}}$. Also from this follows that $latex (\mathsf{FCD})$ preserves all suprema and $latex (\mathsf{RLD})_{\mathrm{in}}$ preserves all infima. See Algebraic General Topology and specifically Funcoids and Reloids online article.

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#galois connection#galois correspondence
Algebraic general topology

A counterexample: Funcoid corresponding to outer reloid

By Victor Porton
On April 22, 2010

I found a counter-example to the following conjecture. Conjecture $latex (\mathsf{FCD}) (\mathsf{RLD})_{\mathrm{out}} f = f$ for every funcoid $latex f$. The counterexample is $latex f = {(=)}|_{\Omega}$ where $latex \Omega$ is the Fréchet filter. See Algebraic General Topology and in particular Funcoids…

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Algebraic general topology

A counterexample against “Meet of discrete funcoids is discrete”

By Victor Porton
On April 21, 2010

I found a counterexample to the following conjecture: Conjecture $latex f\cap^{\mathsf{FCD}} g = f\cap g$ for every binary relations $latex f$ and $latex g$. The counter-example is $latex f = {(=)}|_{\mho}$ and $latex g = \mho\times\mho \setminus f$. I proved $latex f…

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Algebraic general topology Filters Open problems

A theorem generalized

By Victor Porton
On April 20, 2010

I generalized a theorem in the preprint article “Filters on posets and generalizations” on my Algebraic General Topology site. The new theorem is formulated as following: Theorem If $latex (\mathfrak{A}; \mathfrak{Z})$ is a join-closed filtrator and $latex \mathfrak{A}$ is a meet-semilattice and…

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#co-completion#completion#core part
Filters Publications

Filters article sent to Moscow Mathematical Journal

By Victor Porton
On April 5, 2010

My second submit to Documenta Mathematica journal of “Filters on Posets and Generalizations” preprint was unanswered in reasonable amount of time. As such I submitted it to an other journal, Moscow Mathematical Journal.

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#Documenta Mathematica#Moscow Mathematical Journal
Uncategorized

I take a vacation in my research work

By Victor Porton
On April 1, 2010

I decided to dedicate my free (of working as a programmer) time to write a book about religion (What book? It will be a surprise.) So in a few nearby months I am going to not continue my math research. I am…

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#vacation
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  • SCIENCE
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  • SCIENCE
  • Home
    • Blog
    • Soft
  • Algebraic General Topology
    • Paperback
    • Ebook
    • PDF
  • Axiomatic Theory of Formulas
    • Paperback
    • Ebook
    • PDF
  • Limit of a Discontinuous Function
  • More
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  • Prize