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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”.

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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.

October 13, 2018 / porton

Poset of unfixed filters

I defined partial order on the set of unfixed filters and researched basic properties of this poset.

Also some minor results about equivalence of filters.

See my book.

October 11, 2018 / porton

Rebase of filters and equivalent filters

I added a few new propositions into “Equivalent filters and rebase of filters” section (now located in the chapter “Filters and filtrators”) of my book.

I also define “unfixed filters” as the equivalence classes of (small) filters on sets.

This is a step forward to also define “unfixed funcoids” and “unfixed reloids”.