The injective hull of ultra-quasi-metric versus q-hyperconvex hull of quasi-metric space

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Peer-Reviewed Research
  • SDG 8
  • SDG 7
  • Abstract:

    For any partially ordered set equipped with its natural T0-quasi-metric (T0-ultra-quasi-metric), we study the connection between the ultra-quasi-metrically injective hull and the q-hyperconvex hull. We also observe that for a partially ordered set, its Dedekind-MacNeille completion coincides exactly with the ultra-quasi-metric injective hull of its natural T0-ultra-quasi metric.