Redundancy of multiset topological spaces

TL;DR

This paper demonstrates that multiset topologies are redundant by establishing an isomorphism with a simpler power set structure, suggesting they are unnecessary in theory.

Contribution

It proves the redundancy of multiset topologies by showing their isomorphism to a standard power set, simplifying the theoretical framework.

Findings

Multiset topologies are isomorphic to a power set structure.

Multiset topologies are redundant and unnecessary in theory.

Establishes a complement-preserving isomorphism between the two structures.

Abstract

In this paper, we prove the redundancies of multiset topologies. It is shown that there is a complement preserving isomorphism between $(P^\star(U),\sqsubseteq)$ and $(\mathcal{P}(X\times\mathbb{N}),\subseteq)$. It therefore follows that multiset topologies are superfluous and unnecessary in the theoretical view point.