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1 results

  • Persistent properties from the Gromov–Hausdorff viewpoint

  • Part of
  • Abdul Gaffar Khan, Carlos Arnoldo Morales, Tarun Das
  • Journal:
    Proceedings of the Edinburgh Mathematical Society / Volume 67 / Issue 4 / November 2024
    Published online by Cambridge University Press:
    02 December 2024, pp. 1229-1240
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  • In this paper, we introduce topologically IGH-stable, IGH-persistent,average IGH-persistent and pointwise weakly topologically IGH-stable homeomorphisms of compact metric spaces. We prove that every topologically IGH-stable homeomorphism is topologically stable and every expansive topologically stable homeomorphism of a compact manifold is topologically IGH-stable. We further prove that every equicontinuous pointwise weakly topologically IGH-stable homeomorphism is IGH-persistent and every pointwise minimally expansive IGH-persistent homeomorphism is pointwise weakly topologically IGH-stable. Finally, we prove that every mean equicontinuous pointwise weakly topologically IGH-stable homeomorphism is average IGH-persistent.