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October 22, 2018 / porton

“Unfixed filters” research now in the book volume-1

I essentially finished my research of unfixed filters.

I moved all research of unfixed filters to volume-1.pdf. Particularly now it contains subsections “The lattice of unfixed filters” and “Principal unfixed filters and filtrator of unfixed filters”.

Now I am going to research unfixed reloids and unfixed funcoids (yet to be defined).

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October 22, 2018 / porton

Filters on a lattice are a lattice

I’ve proved that filters on a lattice are a lattice.

See my book.

October 21, 2018 / porton

I strengthened a theorem

I strengthened a theorem: It is easily provable that every atomistic poset is strongly separable (see my book).

It is a trivial result but I had a weaker theorem in my book before today.

October 19, 2018 / porton

Math volunteer job

I welcome you to the following math research volunteer job:

Participate in writing my math research book (volumes 1 and 2), a groundbreaking general topology research published in the form of a freely downloadable book:

  • implement existing ideas, propose new ideas
  • develop new theories
  • solve open problems
  • write and rewrite the book and other files
  • check for errors
  • help with book LaTeX formatting
  • represent the research at scientific conferences

You can do all of the above or any particular thing, dependently on your mood.

Required skills:

  • basic general topology
  • LaTeX
  • Git

More desired skills:

  • advanced general topology
October 18, 2018 / porton

An error in my book

I erroneously concluded (section “Distributivity of the Lattice of Filters” of my book) that

the base of every primary filtrator over a distributive lattice which is an ideal base is a co-frame.

Really it can be not a complete lattice, as in the example of the lattice of the poset of all small (belonging to a Grothendieck universe) sets.

I will update my book soon.

October 18, 2018 / porton

A theorem with a diagram about unfixed filters

I’ve added to my book a theorem with a triangular diagram of isomorphisms about representing filters on a set as unfixed filters or as filters on the poset of all small (belonging to a Grothendieck universe) sets.

The theorem is in the subsection “The diagram for unfixed filters”.

October 18, 2018 / porton

Error in my book

There is an error in recently added section “Equivalent filters and rebase of filters” of my math book.

I uploaded a new version of the book with red font error notice.

The error seems not to be serious, however. I think all this can be corrected. Other sections of the book are not affected at all.