Geodesic
A countably compact, separable space which is not absolutely countably compact
Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 1, pp. 197-201

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We construct a space having the properties in the title, and with the same technique, a countably compact $T_2$ topological group which is not absolutely countably compact.
Classification : 22A05, 54B10, 54D20, 54G20, 54H11
Keywords: countably compact; absolutely countably compact; topological group; Franklin-Rajagopalan space 
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Vaughan, Jerry E. A countably compact, separable space which is not absolutely countably compact. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 1, pp. 197-201. http://geodesic.mathdoc.fr/item/CMUC_1995__36_1_a20/