### An important conjecture about funcoids. Version 2

This conjecture appeared to be false. Now I propose an alternative conjecture: Let $latex A$, $latex B$ be sets. Conjecture Funcoids $latex f$ from $latex A$ to $latex B$ bijectively corresponds to the sets $latex R$ of pairs $latex (\mathcal{X}; \mathcal{Y})$ of…

### An important conjecture about funcoids

Just a few minutes ago I’ve formulated a new important conjecture about funcoids: Let $latex A$, $latex B$ be sets. Conjecture Funcoids $latex f$ from $latex A$ to $latex B$ bijectively corresponds to the sets $latex R$ of pairs $latex (\mathcal{X}; \mathcal{Y})$…

### Join of transitive reloids (a conjecture in uniformity theory)

Conjecture Join of a set $latex S$ on the lattice of transitive reloids is the join (on the lattice of reloids) of all compositions of finite sequences of elements of $latex S$. It was expired by theorem 2.2 in “Hans Weber. On…

### Preservation of properties of funcoids and reloids by their relationships

I have added a new section “Properties preserved by relationships” to my math research book. This section considers (in the form of theorems and conjectures) whether properties (reflexivity, symmetry, transitivity) of funcoids and reloids are preserved an reflected by their relationships (functions…

### New version of my math research book

I’ve released a new version of my free math ebook. The main feature of this new release is chapter “Alternative representations of binary relations” where I essentially claim that the following are the same: binary relations pointfree funcoids between powersets Galois connections…