An equivalence of results in $C^*$-algebra valued b-metric and b-metric spaces

• Autores: Nguyen Van Dung, Vo Thi le Hang, Diana Dolicanin Djekic
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 18, Nº. 2, 2017, págs. 241-253
• Idioma: inglés
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• Resumen

  • We construct a $b$-metric from a given $C^*$-algebra-valued $b$-metric and prove some equivalences between them. Then we show that not only fixed point results but also topological properties on $C^*$-algebra-valued $b$-metric spaces may be deduced from certain results in $b$-metric spaces. In particular, every $C^*$-algebra-valued $b$-metric space is metrizable.