Density of periodic orbits for topological Anosov flows

Let $M$ be the underlying manifold and let $\mathcal{TA}\mathcal{F}(M)$ denote the class of topological Anosov flows on $M$. A periodic orbit is an orbit of a point that returns to itself after a positive time.

Density of periodic orbits. Every topological Anosov flow $\theta\in\mathcal{TA}\mathcal{F}(M)$ possesses a dense set of periodic orbits.

Dense periodic orbits are a fundamental hallmark of classical Anosov dynamics. The source proposes this inheritance for the topological class but gives no proof or resolution.