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Algebraic General Topology
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funcoids and reloids, a generalization of proximities and uniformities
funcoids and reloids, a generalization of proximities and uniformities

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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…
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I proved that filters on a lattice are a lattice. See my book.
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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.
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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…
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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…
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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…
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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…
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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.
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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.
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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.
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