Closed graph and open mapping theorems for normed cones

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.