Abstract
In this article, we mainly show that a finite product of ordinals is hereditarily dually discrete. This gives an affirmative answer to a problem posed by Peng in [16, Problem 12]. By this conclusion and a known conclusion we have that if Y is a subspace of the product of a finitely many ordinals, then Y is hereditarily a Lindelöf D-space if and only if Y has countable spread.
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