Topological well-orderedness for root-cause identification in networks: canonical explanations via upper-bound graphs

• Kandemir, Mustafa Burç ^[1]
  1. [1] Muğla University

     Muğla University

     Turquía

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 27, Nº. 2, 2026
• Idioma: inglés
• DOI: 10.4995/agt.25340
• Enlaces
  • Texto completo
• Resumen

  • We introduce topological well-orderedness (TWO) for triples ( X , T , ≤ ) , requiring that every nonempty open set admits a least element. For each open set U, we define the upper-bound graph UB(U) by joining x , y ∈ U whenever they share an upper bound in U, and study its clique complex together with an associated upper-bound simplicial complex. Our main results show that TWO yields canonical dominating-vertex certificates, implying that these complexes are cones and hence contractible. Consequently, their reduced homology vanishes in all dimensions, providing a simple topological invariant for well-ordered open-set dynamics. We further examine filtrations induced by nested observations and discuss implications for persistent homology, including stability under monotone unions. A toy network-diagnostics example illustrates how the framework supports canonical explanations in root-cause identification.

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