### Binary relations are essentially the same as pointfree funcoids between powersets

After this Math.StackExchange question I have proved that binary relations are essentially the same as pointfree funcoids between powersets. Full proof is available in my draft book. The most interesting aspect of this is that is that we can construct filtrator with…

### Ideals, free stars, and mixers in my book

I wrote a section on ideals, free stars, and mixers in my book. Now free stars (among with ideals and mixers) are studied as first class objects, being shown isomorphic to filters on posets. In (not so far) future it should allow…

### I’ve rewritten my book in LyX

Previously I wrote my research monograph with TeXmacs word processors. TeXmacs is a very good program. However annoying bugs of TeXmacs (incorrect file “saved” status, failure to work well when multiple windows with the same document are opened, etc.) and also its…

### An example of a separable poset with certain property

With help of sci.math crowd it was demonstrated an example that there exist a (finite) poset, which is separable (in the sense defined in this book), but \$latex \star x \subseteq \star y\$ does not imply \$latex x \sqsubseteq y\$ (where \$latex…

### Modular hyperlinked mathematics (as a replacement of books)

The following are suggestions how to replace math books with hyperlinked modules, in general, and particularly suggestions how to support it in a future version of TeXmacs software. TeXmacs is an advanced math writing software, and the easiest way to implement my…

### About topological structures corresponding to partial order

Intuitively (not in the sense of comparing cardinalities, but in some other sense), the set of natural numbers is less than the set of whole numbers, which is less than the set of rational numbers, which is less than the set of…

### Generalized Fréchet filters

Just a few minutes ago I conceived a definition of generalized Fréchet filters with definition for every poset on which filters are considered (however, I have not yet calculated the class of posets for which generalized Fréchet filter is defined; it should…

### Proximities are reflexive, symmetric, transitive funcoids

I’ve done a little discovery today: Proximities are the same reflexive, symmetric, transitive funcoids. For now I leave to prove this as an exercise for a reader. But later I am going to include this theorem into the book I am writing.

### I withdrew my article from a journal

My article was accepted for publication in European Journal of Pure and Applied Mathematics, but it didn’t compile with their LaTeX templates. After waiting a reasonable time until they would tackle the problem, I have withdrawn my article and sent it to…