On the semi-uniformity of bornological convergence

Abstract

When in the construction of the ρ-Hausdorff distance the balls with finite radius are replaced with an arbitrary ideal of bounded sets we no longer obtain a uniformity, but a semi-uniformity. In this paper we study the uniform reflection of this structure and its properties.

Keywords: Semi-uniformity, pretopology, bornology, bornological convergence, Hausdorff distance.