Quasinormed Cones and Bicompletion Isometries

Abstract

Since (X, e_(p_j )) is an extended quasi-metric cone, we demonstrate how any quasi-norm p_jon an actual cancellative cone X naturally implies an extended quasi-metric e_(p_j ) on that cone. We demonstrate that bicompletion respects the structure of a quasi-normalized cone under bijective isometries. In fact, we find that isometries are not generally injective in this case. In addition, a few situations are shown.