### I take a vacation in my research work

I decided to dedicate my free (of working as a programmer) time to write a book about religion (What book? It will be a surprise.) So in a few nearby months I am going to not continue my math research. I am…

### Strong vs weak partitioning – counterexample

My problem whether weak partitioning and strong partitioning of a complete lattice are the same was solved by counter-example by François G. Dorais. Remains open whether strong and weak partitioning of a filter object is the same.

### Principal filters are center – solved

I have proved this conjecture: Theorem 1 If \$latex {\mathfrak{F}}&fg=000000\$ is the set of filter objects on a set \$latex {U}&fg=000000\$ then \$latex {U}&fg=000000\$ is the center of the lattice \$latex {\mathfrak{F}}&fg=000000\$. (Or equivalently: The set of principal filters on a set…

### Formalistics of generalization

In the framework of ZF formally considered generalizations, such as whole numbers generalizing natural number, rational numbers generalizing whole numbers, real numbers generalizing rational numbers, complex numbers generalizing real numbers, etc. The formal consideration of this may be especially useful for computer…

### My new math blog

I abandoned my old blogs at my own site and moved to WordPress.com. This is my new math blog. Here I will tell about my math research.