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This paper is concerned with the      ( ω  1 , ω  1 ∗  ) ({\omega _1},\omega _1^{\ast })      -gaps of F. Hausdorff and the topological spaces defined from them by Eric van Douwen. We construct special gaps in order that the associated gap spaces will have interesting topological properties. For example, the gap spaces we construct show that in certain models of set theory, there exist countably compact, first countable, separable, nonnormal      T 2 {T_2}      -spaces.

On first countable, countably compact spaces. I. (𝜔₁,𝜔*₁)-gaps