Existence of a space filled with an arbitrary finite number of mutually disjoint self-similar spaces

TL;DR

This paper establishes a sufficient topological condition under which a space can be completely filled with a finite number of mutually disjoint self-similar spaces, advancing understanding of space partitioning in topology.

Contribution

It introduces a novel sufficient condition for partitioning a space into disjoint self-similar subsets, expanding the theoretical framework of self-similarity in topology.

Findings

Identifies a specific topological condition for space partitioning

Demonstrates the possibility of filling a space with disjoint self-similar spaces

Provides theoretical groundwork for further research in space decomposition

Abstract

We discuss a sufficient condition for a space to be filled with an arbitrary finite number of self-similar spaces using a topological concept.