On sncc-Inheritance of Pointwise Almost Periodicity in Flows - Dai, Xiongping (Topology Proceedings, 2024)
Let H be a subnormal co-compact closed subgroup of a Hausdorff topological group T and X a compact Hausdorff space. We prove the inheritance theorem: A point of X is almost periodic (a.p.) for T X if and only if it is a.p. for H X. Moreover, if T X is minimal with H T, then O_H: X → 2^X, x H x is a continuous mapping, and T X / H is an a.p. nontrivial factor of T X if and only if T X × T / H is not minimal.