A product space of {0, 1} and an abstract polycrystal

TL;DR

This paper introduces an abstract polycrystal concept derived from partitions of infinite product spaces of {0,1}, revealing self-similar structures within the decomposition space.

Contribution

It presents a novel framework linking product space partitions to the structure of abstract polycrystals and their self-similar decomposition spaces.

Findings

Defines an abstract polycrystal from product space partitions

Shows the decomposition space is self-similar

Connects product space topology with polycrystal structure

Abstract

A partition of a $\Lambda (Card\Lambda \succ \aleph_0)$-product space of $\{0,1\}$ defines an abstract polycrystal composed of abstract singlecrystals a decomposition space (space of equivalence classes) of each of which is self-similar.