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

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.