### New chapter in my research monograph

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.

### Change of terminology

I 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.

### Totally bounded reloids, a generalization of totally bounded uniform spaces

This 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 $latex \mathrm{Ob}\, f$…

### “Simple product”, a new kind of product of funcoids

Today 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}…

### A partial proof of “Partitioning a filter into ultrafilters” conjecture

I’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.