Coarse direct products and property {C}

TL;DR

This paper demonstrates that coarse property C and the coarse analog of Dydak's countable asymptotic dimension are preserved under finite coarse direct products, linking them to straight finite decomposition complexity.

Contribution

It establishes the preservation of coarse property C and the coarse analog of Dydak's countable asymptotic dimension under finite coarse direct products, connecting these concepts to finite decomposition complexity.

Findings

Coarse property C is preserved by finite coarse direct products.

The coarse analog of Dydak's countable asymptotic dimension is equivalent to coarse straight finite decomposition complexity.

These properties are preserved under direct products.

Abstract

We show that coarse property C is preserved by finite coarse direct products. We also show that the coarse analog of Dydak's countable asymptotic dimension is equivalent to the coarse version of straight finite decomposition complexity and is therefore preserved by direct products.