I’ve added new chapter 11 “Total boundness of reloids” to my book “Algebraic General Topology. Volume 1”. It expresses several kinds of boundness of reloids, which are however the same total boundness in the special case of uniform spaces.

read moreI realized that the terms “discrete funcoid” and “discrete reloid” conflict with conventional usage of “discrete topology” and “discrete uniformity”. Thus I have renamed them into “principal funcoid” and “principal reloid”. See my research monograph.

read moreThis is a straightforward generalization of the customary definition of totally bounded sets on uniform spaces: Definition Reloid $latex f$ is totally bounded iff for every $latex E \in \mathrm{GR}\, f$ there exists a finite cover $latex S$ of $latex \mathrm{Ob}\, f$…

read moreToday I’ve discovered a new kind of product of funcoids which I call “simple product”. It is defined by the formulas $latex \left\langle \prod^{(S)}f \right\rangle x = \lambda i \in \mathrm{dom}\, f: \langle f_i \rangle x_i$ and $latex \left\langle \left( \prod^{(S)}f \right)^{-1}…

read moreI’ve put a partial partial proof of “Every filter on a set can be strongly partitioned into ultrafilters” conjecture at PlanetMath. Please collaborate in solving this conjecture.

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