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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
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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.

October 17, 2018 / porton

New important theorem

I have proved that \mathscr{S} is an order isomorphism from the poset of unfixed filters to the poset of filters on the poset of small sets.

This reveals the importance of the poset of filters on the poset of small sets.

See the new version of my book.

October 15, 2018 / porton

New version of my math book (“Equivalent filters and rebase of filters” section)

I have added to my book, section “Equivalent filters and rebase of filters” some new results. Particularly I added “Rebase of unfixed filters” subsection.

It remains to research the properties of the lattice of unfixed filters.

October 13, 2018 / porton

Equivalence filters and the lattice of filters on the poset of small sets

Equivalence of filters can be described in terms of the lattice of filters on the poset of small sets.

See new subsection “Embedding into the lattice of filters on small” in my book.