I proved the following theorem: Theorem If $latex S$ is a generalized filter base then $latex \left\langle f \right\rangle \bigcap{\nobreak}^{\mathfrak{F}} S = \bigcap {\nobreak}^{\mathfrak{F}} \left\langle\left\langle f \right\rangle \right\rangle S$ for every funcoid $latex f$. The proof (presented in updated version of this…

read moreI am now trying to prove or disprove this innocently looking but somehow surprisingly hard conjecture: Conjecture If $latex S$ is a generalized filter base then $latex \left\langle f \right\rangle \bigcap{\nobreak}^{\mathfrak{F}} S = \bigcap {\nobreak}^{\mathfrak{F}} \left\langle\left\langle f \right\rangle \right\rangle S$ for every…

read moreMy draft article “Orderings of filters in terms of reloids. Extensions of Rudin-Keisler ordering” is updated. Read here. Now it uses the language of basic category theory. It is yet not carefully checked for errors.

read moreIn the past I considered my purpose to exactly and directly follow commandments of Bible. I had some purposes hardly set as the aim of my life. My life was driven by these purposes not by my wish or my heart. I…

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