The topological Hopf brushing conjecture

A brushing is a flow without fixed points. A closed topological manifold is a compact manifold in the topological category, and its Euler characteristic is denoted $c7(M)$.

Topological Hopf brushing conjecture. A closed topological manifold with vanishing Euler characteristic admits a brushing.

This is presented as a topological analogue of Hopf's smooth theorem. Existing path-field results do not supply the required integration into a flow, so the assertion remains hypothetical in the source.