Universal topological representation of geometric patterns

TL;DR

This paper introduces a universal topological framework for representing geometric patterns in condensed matter, using decomposition spaces of infinite product spaces to characterize their structures.

Contribution

It presents a novel topological method that universally encodes geometric structures through decomposition spaces of infinite binary product spaces.

Findings

Provides a universal topological representation for geometric patterns.

Connects geometric structures with specific partitions in topological spaces.

Offers a new perspective for analyzing condensed matter geometries.

Abstract

We discuss here geometric structures of condensed matters by means of a fundamental topological method. Any geometric pattern can be universally represented by a decomposition space of a topological space consisting of the infinite product space of 0 and 1, in which a partition with a specific topological structure determines a character of each geometric structure.