• 호남수학학술지
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• 제26권2호
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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.

• 충청수학회지
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• 제8권1호
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• pp.19-27
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• 1995

In 1974 H.Herrlich invented nearness spaces, a very fruitful concept which enables one to unify topological aspects. In this paper, we introduce the Lindel$\ddot{o}$f nearness structure, countably bounded nearness structure and countably totally bounded nearness structure. And we show that (X, ${\xi}_L$) is concrete and complete if and only if ${\xi}_L={\xi}_t$ in a symmetric topological space (X, t). Also we show that the following are equivalent in a symmetric topological space (X, t): (1) (X, ${\xi}_L$) is countably totally bounded. (2) (X, ${\xi}_t$) is countably totally bounded. (3) (X, t) is countably compact.