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Micronization – the first attempt to define

This is my first attempt to define micronization.

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

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\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 Image may be NSFW.
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f
is a strict partial order, Image may be NSFW.
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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.


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