A not metrizable space filled with any n mutually disjoint self-similar spaces

TL;DR

The paper investigates a specific topological space constructed as a Lambda-product of {0,1}, demonstrating that it can be partitioned into n disjoint self-similar subspaces, regardless of n.

Contribution

It introduces a novel construction of a non-metrizable space that can be decomposed into any number of disjoint self-similar components.

Findings

The space is not metrizable.

It admits partitions into any number of disjoint self-similar spaces.

Each component in the partition is self-similar.

Abstract

A Lambda (Card Lambda > aleph)-product space of {0,1} has a partition {X1,...,Xn} for any n a decomposition space of each Xi of which is self-similar.(February 16, 2015)