### Pointfree funcoids – a category

I updated the draft of my article “Pointfree Funcoids” at my Algebraic General Topology site. The new version of the article defines pointfree funcoids differently than before: Now a pointfree funcoid may have different posets as its source and destination. So pointfree…

### Generalization in ZF

I wrote short article “Generalization in ZF” accompanied with Isabelle/ZF sources. This is a draft and alpha. I await your comments on both the article and Isabelle sources. I’m sure my Isabelle sources may be substantially improved (and I plan to work…

### A little error corrected

I corrected a small error in “Filters on Posets and Generalizations” article. The error was in Appendix B in the proof of the theorem stating $latex (t;x)\not\in S$ (I messed $latex t$ and $latex \{t\}$.)

### Discrete funcoid which is not complemented

I found an example of a discrete funcoid which is not a complemented element of the lattice of funcoids. Thus the set of discrete funcoids is not the center of the lattice of funcoids, as I conjectured earlier. See the Appendix “Some…

### Pointfree funcoids

I put on the Web the first preliminary draft of my article “Pointfree Funcoids”. It seems that pointfree funcoids is a useful tool to research n-ary (multidimensional as opposed to binary) funcoids which in turn is a useful tool to research operations…

### Two propositions and a conjecture

I added to Funcoids and Reloids article the following two new propositions and a conjecture: Proposition $latex (\mathsf{FCD}) (f\cap^{\mathsf{RLD}} ( \mathcal{A}\times^{\mathsf{RLD}} \mathcal{B})) = (\mathsf{FCD}) f \cap^{\mathsf{FCD}} (\mathcal{A}\times^{\mathsf{FCD}} \mathcal{B})$ for every reloid $latex f$ and filter objects $latex \mathcal{A}$ and $latex \mathcal{B}$. Proposition…

I added the following proposition to the Funcoids and Reloids article: Proposition $latex (\mathsf{FCD})I_{\mathcal{A}}^{\mathsf{RLD}} = I_{\mathcal{A}}^{\mathsf{FCD}}$ for every filter object $latex \mathcal{A}$.
A proof of the following conjecture (now a theorem) was quickly found by me after its formulation: Theorem $latex \left\langle f \right\rangle \mathcal{X} = \bigcap^{\mathfrak{F}} \left\{ \left\langle F \right\rangle \mathcal{X} | F \in \mathrm{up}f \right\}$ for every funcoid $latex f$ and f.o….