A combinatorial approach to certain topological spaces based on minimum complement S-approximation spaces

TL;DR

This paper explores a new topological framework for systems with uncertainty using combinatorial methods on S-approximation spaces, introducing a subclass called $S_ ext{MC}$-approximations and analyzing their topological properties.

Contribution

It introduces the $S_ ext{MC}$-approximation subclass and investigates their topological properties and classifications up to homeomorphism.

Findings

Topological properties of $S_ ext{MC}$-approximations are characterized.

Enumeration of topologies formed by $S_ ext{MC}$-approximations up to homeomorphism.

A combinatorial approach provides new insights into non-inclusion-based systems.

Abstract

An S-approximation space is a novel approach to study systems with uncertainty that are not expressible in terms of inclusion relations. In this work, we further examined these spaces, mostly from a topological point of view by a combinatorial approach. This work also identifies a subclass of these approximation spaces, called $S_\mathcal{MC}$-approximations. Topological properties of this subclass are investigated and finally, the topologies formed by $S_\mathcal{MC}$-approximations are enumerated up to homeomorphism.