Topological Structures of Sets and their Subsets
Abstract
For real application and theoretical investigation of ordinary hypergraphs and non-ordinary hypergraphs, researchers need to establish standard rules and feasible operating methods. We propose a visualization tool for investigating hypergraphs by means of the natural topological structure of finite sets and their subsets, so we are able to construct various non-ordinary hypergraphs, and to reveal topological properties (such as hamiltonian cycles, maximal planar graphs), colorings, connectivity, hypergraph group, isomorphism and homomorphism of hypergraphs.
Cite
@article{arxiv.2503.20167,
title = {Topological Structures of Sets and their Subsets},
author = {Fei Ma and Bing Yao},
journal= {arXiv preprint arXiv:2503.20167},
year = {2025}
}
Comments
We propose a visualization tool for investigating hypergraphs by means of the natural topological structure of finite sets and their subsets, so we are able to construct various non-ordinary hypergraphs, and to reveal topological properties (such as hamiltonian cycles, maximal planar graphs), colorings, connectivity, hypergraph group, isomorphism and homomorphism of hypergraphs