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<p>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 <i>k</i>-connectivity in graphs), connectivity and path-connectivity in topology, and connectivity of elements in a frame.</p>

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What is Connectivity?

  • 期刊论文

  • 发表日期：

    2026年3月22日

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  • Jean F. Du Plessis,
  • Zurab Janelidze,
  • Bernardus A. Wessels

摘要

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.