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arXiv · 2501.19226

What is Connectivity?

Jean F. Du Plessis·Zurab Janelidze·Bernardus A. Wessels
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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.

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Jean F. Du Plessis, Zurab Janelidze, Bernardus A. Wessels. 2025-01-31. What is Connectivity?. https://doi.org/10.1007/s10485-025-09840-0

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