Comment by Gro-Tsen on How should we picture the set of monomial orders (= positive monoid orders on $\mathbb{N}^k$)?

@SamHopkins Thanks! To spell it out explicitly, they explain (prop. 1.7, prop. 3.1 and remark following cor. 4.1) that the set of monomial orders is homeomorphic to the Cantor set.