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).

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

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.

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

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.

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”.

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.

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