Varieties of coarse spaces (Q2305846)

Summary: A class \(\mathfrak{M}\) of coarse spaces is called a variety if \(\mathfrak{M}\) is closed under the formation of subspaces, coarse images, and products. We classify the varieties of coarse spaces and, in particular, show that if a variety \(\mathfrak{M}\) contains an unbounded metric space then \(\mathfrak{M}\) is the variety of all coarse spaces.