• Honam Mathematical Journal
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• v.26 no.2
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• pp.209-218
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• 2004

On the analogy of total countable compactness, we study interesting subfamilies in the class of pseudocompact spaces. We show relationships between totally pseudocompact spaces, sequentially pseudocompact spaces, and DFCC spaces. We also prove relationships among densely ${\xi}$-pseudocompact, ${\xi}$-pseudocompact, and countably pracompact spaces. As a productive result on countably pracompact spaces, we will prove that if X is a countably pracompact space and Y is a countably pracompact ${\kappa}$-space, then $X{\times}Y$ is count ably pracompact.