Metrization of idempotent semiring of topological rings
[EN]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) s...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/227664 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/227664 |
| Access Level: | acceso abierto |
| Palabra clave: | H⁺-pseudovaluation H⁺-norm Topological completely regular (algebraic) semiring B-lattice Uniformity structure |
| Sumario: | [EN]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. |
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