• Closed Graph and Open Mapping Theorems for Normed Cones

• # Fulltext

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

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

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 4
September 2019