  In this short note, for countably infinite amenable group actions, we provide
topological proofs for the following results: Bowen topological entropy
(dimensional entropy) of the whole space equals the usual topological entropy
along tempered F{\o}lner sequences; the Hausdorff dimension of an amenable
subshift (for certain metric associated to some F{\o}lner sequence) equals its
topological entropy. This answers questions by Zheng and Chen (Israel Journal
of Mathematics 212 (2016), 895-911) and Simpson (Theory Comput. Syst. 56
(2015), 527-543).
