• Closed Graph and Open Mapping Theorems for Normed Cones

    • Fulltext

       

        Click here to view fulltext PDF


      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/118/02/0245-0254

    • 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

    • Editorial Note on Continuous Article Publication

      Posted on July 25, 2019

      Click here for Editorial Note on CAP Mode

© 2017-2019 Indian Academy of Sciences, Bengaluru.