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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 added to my online research book the following theorem: Theorem Let be a distributive lattice with least element. Let . If exists, then also exists and . The user quasi of Math.SE has helped me with the proof.

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I’ve published in my blog a new theorem. The proof was with an error (see the previous edited post)!

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I knew that composition of two complete funcoids is complete. But now I’ve found that for to be complete it’s enough to be complete. The proof which I missed for years is rather trivial: Thus is complete. I will amend my book when (sic!) it will be…

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I have proved (see new version of my book) the following proposition. (It is a special case of my erroneous theorem which I proposed earlier.) Proposition For , a finite set and a function there exists (obviously unique) such that for and for . This…

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I found the exact error noticed in Error in my theorem post. The error was that I claimed that infimum of a greater set is greater (while in reality it’s lesser). I will delete the erroneous theorem from my book soon.

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It seems that there is an error in proof of this theorem. Alleged counter-example: and for infinite sets and . I am now attempting to locate the error in the proof.

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I have proved (and added to my online book) the following theorem: Theorem Let and . Then there is an (obviously unique) funcoid such that for nontrivial ultrafilters and for After I started to prove it, it took about a hour or like this to finish the…

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I proved the following (in)equalities, solving my open problem which stood for a few months: The proof is currently available in the section “Some inequalities” of this PDF file. Note that earlier I put online some erroneous proof related to this.

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I have published What is physical reality? blog post in my other blog. The post is philosophical.

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I proved that and so disproved one of my conjectures. The proof is currently available in the section “Some inequalities” of this PDF file. The proof isn’t yet thoroughly checked for errors. Note that I have not yet proved , but the proof is expected to…
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