# Micronization – the first attempt to define

This is my first attempt to define micronization.

Definition Let $f$ is a binary relation between sets $A$ and $B$. micronization $\mu (f)$ of $f$ is the complete funcoid defined by the formula (for every $x \in A$)

$\left\langle \mu (f) \right\rangle \left\{ x \right\} = \bigcap \left\{ \uparrow^B \left( f x \setminus f y \right) \hspace{1em} | \hspace{1em} \left( x ; y \right) \in f \right\}.$

Conjecture If $f$ is a strict partial order, $S^{\ast} (\mu (f)) = f$.

The idea of micronization is that it transforms a “global” relation (such as a strict partial order) into a “local” space (something like a topology).

This my definition probably can be generalized for funcoids instead of binary relations.