• Closed Graph and Open Mapping Theorems for Normed Cones

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    • Keywords


      Extended quasi-pseudo-metric; quasi-normed cone; continuous mapping; left(right) 𝐾-completeness; closed graph; open mapping.

    • Abstract


      A quasi-normed cone is a pair $(X, p)$ such that 𝑋 is a (not necessarily cancellative) cone and 𝑞 is a quasi-norm on 𝑋. The aim of this paper is to prove a closed graph and an open mapping type theorem for quasi-normed cones. This is done with the help of appropriate notions of completeness, continuity and openness that arise in a natural way from the setting of bitopological spaces.

    • Author Affiliations


      Oscar Valero1

      1. Departamento de Ciencias Matemáticas e Informática, Universidad de las Islas Baleares, Edificio Anselm Turmeda, 07122, Palma de Mallorca, Baleares, Spain
    • Dates

  • Proceedings – Mathematical Sciences | News

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