Universality Property and Dimension for Frames

Abstract

The universality property plays an important role in the field of frames and the notion of saturated class of frames is combined with this property (see Dube et al. (Topology and its Applications 160, 2454–2464, 2013); Iliadis (Topology and its Applications 179, 99–110, 2015) and Iliadis (Topology and its Applications 201, 92–109, 18)). In this paper, we continue such a study, introducing and studying the notion of saturated class of bases for frames. Based on the notions of the small inductive dimension, frind, for frames, which is inserted in Georgiou et al. (2019), and the saturated class of bases, we define the base dimension like-function of the type frind for frames, and prove that in a class of bases which is characterized by this dimension there exist universal elements.