Dense, sequentially continuous maps on dyadic compacta

We prove in ZFC that for every sequentially continuous ω-dense function f which maps a dyadic compactum onto a Tychonoff space Y, there exists a closed subspace Z ⊆ Dτ such that f[Z] = f[Dτ] and the restriction of f to Z is continuous. Moreover, the range of every such mapping f is a dyadic compactum.