Nonstandard methods in large-scale topology II

Abstract

This paper is a sequel of Imamura (2019) (arXiv:1711.01609) where we set up a framework of nonstandard large-scale topology. In the present paper, we apply our framework to various topics in large-scale topology: spaces having with both small-scale and large-scale structures, large-scale structures on nonstandard extensions, size properties of subsets of coarse spaces, and coarse hyperspaces.