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compact; countably compact; absolutely countably compact; hereditarily absolutely countably compact; $\omega $-bounded; countable tightness; sequential space
We show that the product of a compact, sequential $T_2$ space with an hereditarily absolutely countably compact $T_3$ space is hereditarily absolutely countably compact, and further that the product of a compact $T_2$ space of countable tightness with an hereditarily absolutely countably compact $\omega$-bounded $T_3$ space is hereditarily absolutely countably compact.
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