What is Connectivity?
General Topology
2026-05-11 v2 Category Theory
Rings and Algebras
Abstract
In this paper, we explore a taxonomy of connectivity for space-like structures. It is inspired by isolating posets of connected pieces of a space and examining its embedding in the ambient space. The taxonomy includes in its scope all standard notions of connectivity in point-set and point-free contexts, such as connectivity in graphs and hypergraphs (as well as k-connectivity in graphs), connectivity and path-connectivity in topology, and connectivity of elements in a frame.
Cite
@article{arxiv.2501.19226,
title = {What is Connectivity?},
author = {Jean F. Du Plessis and Zurab Janelidze and Bernardus A. Wessels},
journal= {arXiv preprint arXiv:2501.19226},
year = {2026}
}
Comments
22 pages, 13 figures, v2 fixed some figure referencing