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.
@article{118953, author = {Maddalena Bonanzinga}, title = {On the product of a compact space with an hereditarily absolutely countably compact space}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {38}, year = {1997}, pages = {557-562}, zbl = {0937.54013}, mrnumber = {1485076}, language = {en}, url = {http://dml.mathdoc.fr/item/118953} }
Bonanzinga, Maddalena. On the product of a compact space with an hereditarily absolutely countably compact space. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) pp. 557-562. http://gdmltest.u-ga.fr/item/118953/
On bicompacta hereditarily satisfying the Souslin condition. Tightness and free sequences, Soviet Math. Dokl. 12 (1971), 1253-1257. (1971)
On compact space of countable tightness, Proc. Amer. Math. Soc. 105 (1989), 756-764. (1989) | MR 0930252
Preservation and reflection of properties acc and hacc, Comment. Math. Univ. Carolinae 37,1 (1996), 147-153. (1996) | MR 1396166 | Zbl 0917.54027
The integers and topology, Handbook Set-theoretic Topology, K. Kunen and J.E. Vaughan Eds., Elsevier Sci. Publ. (1984), 111-167. (1984) | MR 0776619 | Zbl 0561.54004
General Topology, Warszawa (1977). (1977) | MR 0500780 | Zbl 0373.54002
Quasi-uniform spaces, Marcel Dekker, New York, 1982. | MR 0660063 | Zbl 0583.54017
Linearly ordered topological spaces, Proc. Amer. Math. Soc. 24 (1970), 197-203. (1970) | MR 0250272 | Zbl 0203.55104
On the tightness and the Suslin number of $exp X$ and of a product of spaces, Soviet Math. Dokl. 13 (1972), 496-499. (1972)
Absolutely countably compact spaces, Topology and Appl. 58 (1994), 81-92. (1994) | MR 1280711 | Zbl 0801.54021
A countably compact topological group which is not absolutely countably compact, Questions and Answers 11 (1993), 173-176. (1993) | MR 1234212 | Zbl 0808.54025
Small uncountable cardinals and topology, Open Problems in Topology, J. van Mill, G.M. Reed Eds., North-Holland, Amsterdam (1990), 195-218. (1990) | MR 1078647
On the product of a compact space with an absolutely compact space, Papers on General Topology and Applications, Annals of the New York Academy of Sciences 788 (1996), 203-208. (1996) | MR 1460834