2025/01/31 by Plessis, Jean F. Du, Janelidze, Zurab, Wessels, Bernardus A.
#06A06 #06B23 #06D22 #18A40 #54D05 #Category Theory (math.CT) #FOS: Mathematics #General Topology (math.GN) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2501.19226
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.