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Vietnam Journal of Mathematics 35:2(2007) 169-175  Hausdorff First Countable, Countably Compact Space is $\Omega$ Bounded Nuno C. Freire and M. F. Veiga Abstract.  In this paper we obtain an answer to the question in Problem 288, the book Open Problems in Topology by Jan van Mill and George M. Reed, p. 131. Namely, we prove that a Hausdorff first countable, countably compact topological space is $\Omega$-bounded. We also point out errors occurring in the literature concerning the Ostaszewski spaces.   2000 Mathematics Subject Classification: 54A35, 54D45, 54A25. Keywords: $\omega $-bounded, countably compact.

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