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<p>This paper introduces the concept of partial metric spaces on effect algebras considering the axiom of “nonzero self-distances”. Partial metric spaces for every state defined on effect algebras are obtained and their properties are investigated. It is also proved that each partial metric space gives rise to a metric space on effect algebras. Further, it is proved that the partial metric spaces on effect algebras are complete. 0-completeness characterization of partial metric spaces is also discussed. Convexity and completeness of the obtained metric space are also discussed.</p>

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Partial metric spaces on effect algebras

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • Sarvesh Kumar Mishra,
  • Mukesh Kumar Shukla,
  • Akhilesh Kumar Singh

摘要

This paper introduces the concept of partial metric spaces on effect algebras considering the axiom of “nonzero self-distances”. Partial metric spaces for every state defined on effect algebras are obtained and their properties are investigated. It is also proved that each partial metric space gives rise to a metric space on effect algebras. Further, it is proved that the partial metric spaces on effect algebras are complete. 0-completeness characterization of partial metric spaces is also discussed. Convexity and completeness of the obtained metric space are also discussed.