Metrization of idempotent semiring of topological rings

• Maity, Sunil Kumar ^[1] ; Adak, Gopal ^[1]
  1. [1] University of Calcutta

     University of Calcutta

     India

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 26, Nº. 2, 2025, págs. 725-749
• Idioma: inglés
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• Resumen

  • In this paper, we have introduced natural H+ - pseudovaluation and  H+ -norm on a completely regular semiring making it a topological completely regular (algebraic) semiring and established some necessary and sufficient conditions of metrizability of a topological completely regular (algebraic) semiring. We have generalized the Birkhoff-Kakutani theorem on a first countable topological completely regular (algebraic) semiring. Also we have established that a topological completely regular (algebraic) semiring is metrizable if and only if it is an M- space and its set of additive idempotents is a metrizable Gδ - set in S. Finally we have studied the completion of a b- lattice of topological rings in its uniformity structure.