I removed from my draft sections about “categories under Rel”. The removal happened because I developed a more general and more beautiful theory. The old version is preserved in Git history.
read moreI announced that I have introduces axioms for “restricted identities”, a structure on a category which allows to turn the category into a semigroup (abstracting away objects). But I noticed that these axioms do not fit into concrete examples which I am…
read more“Unfixed filter” section of my book was rewritten for more general lattices instead of old version with a certain lattice of sets.
read moreIn this draft (to be moved into the online book in the future, but the draft is nearing finishing this topic, not including functors between categories with restricted identities) I described axioms and properties of categories with restricted identities. Basically, a category…
read moreI 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…
read moreI’ve proved that filters on a lattice are a lattice. See my book.
read moreI 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.
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Algebraic general topology Category theory Filters General Topology Math on the Web Open problems Pointfree topology Publications
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…
read moreI 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…
read moreI’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…
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